Evaluate $( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$












0












$begingroup$


I need to find the value of



$$( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$



I tried using the identity $a^{3} - b^{3}$ but couldn't reach very far and got stuck.






radicals







share|cite|improve this question











$endgroup$












  • $begingroup$
    What equation? What is there to solve?
    $endgroup$
    – Servaes
    Dec 12 '18 at 17:11










  • $begingroup$
    I mean to find its value.
    $endgroup$
    – navjotjsingh
    Dec 12 '18 at 17:12










  • $begingroup$
    Edited the question. My bad.
    $endgroup$
    – navjotjsingh
    Dec 12 '18 at 17:13










  • $begingroup$
    I'm guessing that $( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$ isn't the answer you're looking for? As that is the value. What kind of expression are you looking for?
    $endgroup$
    – Servaes
    Dec 12 '18 at 17:14












  • $begingroup$
    Is there a specific form you are looking for in the final answer?
    $endgroup$
    – Aditya Dua
    Dec 12 '18 at 17:22
















0












$begingroup$


I need to find the value of



$$( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$



I tried using the identity $a^{3} - b^{3}$ but couldn't reach very far and got stuck.






radicals







share|cite|improve this question











$endgroup$












  • $begingroup$
    What equation? What is there to solve?
    $endgroup$
    – Servaes
    Dec 12 '18 at 17:11










  • $begingroup$
    I mean to find its value.
    $endgroup$
    – navjotjsingh
    Dec 12 '18 at 17:12










  • $begingroup$
    Edited the question. My bad.
    $endgroup$
    – navjotjsingh
    Dec 12 '18 at 17:13










  • $begingroup$
    I'm guessing that $( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$ isn't the answer you're looking for? As that is the value. What kind of expression are you looking for?
    $endgroup$
    – Servaes
    Dec 12 '18 at 17:14












  • $begingroup$
    Is there a specific form you are looking for in the final answer?
    $endgroup$
    – Aditya Dua
    Dec 12 '18 at 17:22














0












0








0


1



$begingroup$


I need to find the value of



$$( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$



I tried using the identity $a^{3} - b^{3}$ but couldn't reach very far and got stuck.






radicals







share|cite|improve this question











$endgroup$




I need to find the value of



$$( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$



I tried using the identity $a^{3} - b^{3}$ but couldn't reach very far and got stuck.






radicals




radicals






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 12 '18 at 17:13







navjotjsingh

















asked Dec 12 '18 at 17:11









navjotjsinghnavjotjsingh

1446




1446












  • $begingroup$
    What equation? What is there to solve?
    $endgroup$
    – Servaes
    Dec 12 '18 at 17:11










  • $begingroup$
    I mean to find its value.
    $endgroup$
    – navjotjsingh
    Dec 12 '18 at 17:12










  • $begingroup$
    Edited the question. My bad.
    $endgroup$
    – navjotjsingh
    Dec 12 '18 at 17:13










  • $begingroup$
    I'm guessing that $( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$ isn't the answer you're looking for? As that is the value. What kind of expression are you looking for?
    $endgroup$
    – Servaes
    Dec 12 '18 at 17:14












  • $begingroup$
    Is there a specific form you are looking for in the final answer?
    $endgroup$
    – Aditya Dua
    Dec 12 '18 at 17:22


















  • $begingroup$
    What equation? What is there to solve?
    $endgroup$
    – Servaes
    Dec 12 '18 at 17:11










  • $begingroup$
    I mean to find its value.
    $endgroup$
    – navjotjsingh
    Dec 12 '18 at 17:12










  • $begingroup$
    Edited the question. My bad.
    $endgroup$
    – navjotjsingh
    Dec 12 '18 at 17:13










  • $begingroup$
    I'm guessing that $( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$ isn't the answer you're looking for? As that is the value. What kind of expression are you looking for?
    $endgroup$
    – Servaes
    Dec 12 '18 at 17:14












  • $begingroup$
    Is there a specific form you are looking for in the final answer?
    $endgroup$
    – Aditya Dua
    Dec 12 '18 at 17:22
















$begingroup$
What equation? What is there to solve?
$endgroup$
– Servaes
Dec 12 '18 at 17:11




$begingroup$
What equation? What is there to solve?
$endgroup$
– Servaes
Dec 12 '18 at 17:11












$begingroup$
I mean to find its value.
$endgroup$
– navjotjsingh
Dec 12 '18 at 17:12




$begingroup$
I mean to find its value.
$endgroup$
– navjotjsingh
Dec 12 '18 at 17:12












$begingroup$
Edited the question. My bad.
$endgroup$
– navjotjsingh
Dec 12 '18 at 17:13




$begingroup$
Edited the question. My bad.
$endgroup$
– navjotjsingh
Dec 12 '18 at 17:13












$begingroup$
I'm guessing that $( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$ isn't the answer you're looking for? As that is the value. What kind of expression are you looking for?
$endgroup$
– Servaes
Dec 12 '18 at 17:14






$begingroup$
I'm guessing that $( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$ isn't the answer you're looking for? As that is the value. What kind of expression are you looking for?
$endgroup$
– Servaes
Dec 12 '18 at 17:14














$begingroup$
Is there a specific form you are looking for in the final answer?
$endgroup$
– Aditya Dua
Dec 12 '18 at 17:22




$begingroup$
Is there a specific form you are looking for in the final answer?
$endgroup$
– Aditya Dua
Dec 12 '18 at 17:22










2 Answers
2






active

oldest

votes


















2












$begingroup$

Let
$$I=( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$
then
$$begin{aligned}
I^2 &=2sqrt{288}^3-2cdot 288sqrt{288-119}+6sqrt{288}cdot 119+2cdot 119sqrt{288-119} \
&= 2sqrt{288}^3-4394+714sqrt{288} \
&= 15480sqrt{2}-4394.
end{aligned}$$
Seeing as this can't be "simplified" further, I suspect the "neatest" form is then
$$I=sqrt{15480sqrt{2}-4394}.$$






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    Let $$x= (sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$



    and $a= (sqrt{288} + sqrt{119})^{3/2}$ and $b= ( sqrt{288} - sqrt{119})^{3/2}$



    then $$a^2+b^2 = 2sqrt{288}^3 + 6sqrt{288}sqrt{119}^2 = 24sqrt{2}(288+3cdot 119)$$ $$ab = (288-119)^{3/2}= 13^3 =2197$$



    so $$x = sqrt{(a-b)^2} = sqrt{15480sqrt{2}-4394}$$






    share|cite|improve this answer









    $endgroup$













      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "69"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });














      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3036960%2fevaluate-sqrt288-sqrt1193-2-sqrt288-sqrt1193-2%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      2












      $begingroup$

      Let
      $$I=( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$
      then
      $$begin{aligned}
      I^2 &=2sqrt{288}^3-2cdot 288sqrt{288-119}+6sqrt{288}cdot 119+2cdot 119sqrt{288-119} \
      &= 2sqrt{288}^3-4394+714sqrt{288} \
      &= 15480sqrt{2}-4394.
      end{aligned}$$
      Seeing as this can't be "simplified" further, I suspect the "neatest" form is then
      $$I=sqrt{15480sqrt{2}-4394}.$$






      share|cite|improve this answer









      $endgroup$


















        2












        $begingroup$

        Let
        $$I=( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$
        then
        $$begin{aligned}
        I^2 &=2sqrt{288}^3-2cdot 288sqrt{288-119}+6sqrt{288}cdot 119+2cdot 119sqrt{288-119} \
        &= 2sqrt{288}^3-4394+714sqrt{288} \
        &= 15480sqrt{2}-4394.
        end{aligned}$$
        Seeing as this can't be "simplified" further, I suspect the "neatest" form is then
        $$I=sqrt{15480sqrt{2}-4394}.$$






        share|cite|improve this answer









        $endgroup$
















          2












          2








          2





          $begingroup$

          Let
          $$I=( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$
          then
          $$begin{aligned}
          I^2 &=2sqrt{288}^3-2cdot 288sqrt{288-119}+6sqrt{288}cdot 119+2cdot 119sqrt{288-119} \
          &= 2sqrt{288}^3-4394+714sqrt{288} \
          &= 15480sqrt{2}-4394.
          end{aligned}$$
          Seeing as this can't be "simplified" further, I suspect the "neatest" form is then
          $$I=sqrt{15480sqrt{2}-4394}.$$






          share|cite|improve this answer









          $endgroup$



          Let
          $$I=( sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$
          then
          $$begin{aligned}
          I^2 &=2sqrt{288}^3-2cdot 288sqrt{288-119}+6sqrt{288}cdot 119+2cdot 119sqrt{288-119} \
          &= 2sqrt{288}^3-4394+714sqrt{288} \
          &= 15480sqrt{2}-4394.
          end{aligned}$$
          Seeing as this can't be "simplified" further, I suspect the "neatest" form is then
          $$I=sqrt{15480sqrt{2}-4394}.$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Dec 12 '18 at 17:27









          Will FisherWill Fisher

          4,0381032




          4,0381032























              1












              $begingroup$

              Let $$x= (sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$



              and $a= (sqrt{288} + sqrt{119})^{3/2}$ and $b= ( sqrt{288} - sqrt{119})^{3/2}$



              then $$a^2+b^2 = 2sqrt{288}^3 + 6sqrt{288}sqrt{119}^2 = 24sqrt{2}(288+3cdot 119)$$ $$ab = (288-119)^{3/2}= 13^3 =2197$$



              so $$x = sqrt{(a-b)^2} = sqrt{15480sqrt{2}-4394}$$






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                Let $$x= (sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$



                and $a= (sqrt{288} + sqrt{119})^{3/2}$ and $b= ( sqrt{288} - sqrt{119})^{3/2}$



                then $$a^2+b^2 = 2sqrt{288}^3 + 6sqrt{288}sqrt{119}^2 = 24sqrt{2}(288+3cdot 119)$$ $$ab = (288-119)^{3/2}= 13^3 =2197$$



                so $$x = sqrt{(a-b)^2} = sqrt{15480sqrt{2}-4394}$$






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  Let $$x= (sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$



                  and $a= (sqrt{288} + sqrt{119})^{3/2}$ and $b= ( sqrt{288} - sqrt{119})^{3/2}$



                  then $$a^2+b^2 = 2sqrt{288}^3 + 6sqrt{288}sqrt{119}^2 = 24sqrt{2}(288+3cdot 119)$$ $$ab = (288-119)^{3/2}= 13^3 =2197$$



                  so $$x = sqrt{(a-b)^2} = sqrt{15480sqrt{2}-4394}$$






                  share|cite|improve this answer









                  $endgroup$



                  Let $$x= (sqrt{288} + sqrt{119})^{3/2} - ( sqrt{288} - sqrt{119})^{3/2}$$



                  and $a= (sqrt{288} + sqrt{119})^{3/2}$ and $b= ( sqrt{288} - sqrt{119})^{3/2}$



                  then $$a^2+b^2 = 2sqrt{288}^3 + 6sqrt{288}sqrt{119}^2 = 24sqrt{2}(288+3cdot 119)$$ $$ab = (288-119)^{3/2}= 13^3 =2197$$



                  so $$x = sqrt{(a-b)^2} = sqrt{15480sqrt{2}-4394}$$







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Dec 12 '18 at 17:29









                  greedoidgreedoid

                  41.2k1150102




                  41.2k1150102






























                      draft saved

                      draft discarded




















































                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3036960%2fevaluate-sqrt288-sqrt1193-2-sqrt288-sqrt1193-2%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -

                      Popular posts from this blog

                      To store a contact into the json file from server.js file using a class in NodeJS

                      Image
                      0 I have created three files -contactPresentation.js, contactService.js, contacts.json. I will run the contactService.js file. And it will navigate to contactPresentation.js file that will only choose an option to either add or display a file. If add(), then add the data into add of service file.And the data will be added to the contacts.json file . And if display(), then display the display() of service file. And the display will take the data from contacts.json file. However, i know my code is flawed. Please correct it . I am also getting an error - this.contacts.push(new ContactService(userName, contactNumber, emailId)); ^ TypeError: Cannot read property 'push' of undefined at ContactService.add (e:NodeJSProjectcontactManager2contactService.js:57:23) at new C
                      Read more

                      Marschland

                      Image
                      Kilometerweite Marsch in den Vier- und Marschlanden am Elbdeich Die Wedeler Marschlandschaft in Schleswig-Holstein Der Hadelner Kanal zur Entwässerung der Marsch Die tief gelegene Marsch und ein Entwässerungskanal Das Schöpfwerk Otterndorf im Land Hadeln zur Entwässerung der Medem verfügte damals bereits über die größte Kreiselpumpe Europas. Das Schöpfwerk in Neuhaus für die Aue und des Neuhaus-Bülkauer Kanals Als Marsch(land) (v. niederdt., altsächs. mersc ) – auch Masch , Mersch oder Schwemmland genannt – bezeichnet man eine nacheiszeitlich entstandene geomorphologische Landform im Gebiet der nordwestdeutschen Küsten und Flüsse sowie vergleichbare Landformen weltweit. Inhaltsverzeichnis 1 Landschaft 2 Entstehung 3 Marschböden 4 Nutzung 5 Marschgebiete in Deutschland 6 Siehe auch 7 Literatur 8 Weblinks 9 Einzelnachweise Landschaft | Marschen sind generell flache Landstriche ohne natürliche Erhebungen. Si
                      Read more

                      Redirect URL with Chrome Remote Debugging Android Devices

                      Image
                      1 How can i redirect an URL with Chrome Remote Debugging Android Devices? like Requestly Chrome extension on desktop. google-chrome debugging url redirect testing share | improve this question edited Nov 24 '18 at 8:16 sachinjain024 14.7k 23 73 129 asked Nov 23 '18 at 16:09 Momen Momen 91 10
                      Read more