सोडोवचें frac{31sqrt{2}+31sqrt{5}}{2sqrt{10}-3}-frac{62sqrt{2}}{3-2sqrt{10}}

$$\frac { 31 \sqrt { 2 } + 31 \sqrt { 5 } } { 2 \sqrt { 10 } - 3 } - \frac { 62 \sqrt { 2 } } { 3 - 2 \sqrt { 10 } }$$

मूल्यांकन करचें

$$15\sqrt{5}+19\sqrt{2}\approx 60.411077348$$

सोडोवणी पांवडे

न्युमरेटर आनी डिनोमिनेटर 2\sqrt{10}+3 न गुणून \frac{31\sqrt{2}+31\sqrt{5}}{2\sqrt{10}-3} चो डिनोमिनेटर रेशनलायझ तर्कसंगत करचो.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{\left(2\sqrt{10}-3\right)\left(2\sqrt{10}+3\right)}-\frac{62\sqrt{2}}{3-2\sqrt{10}}$$

विचारांत घेयात \left(2\sqrt{10}-3\right)\left(2\sqrt{10}+3\right). नेम वापरून गुणाकार विभिन्न चवकोनांत रुपांतरण करूं येताः \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{\left(2\sqrt{10}\right)^{2}-3^{2}}-\frac{62\sqrt{2}}{3-2\sqrt{10}}$$

\left(2\sqrt{10}\right)^{2} विस्तारीत करचो.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{2^{2}\left(\sqrt{10}\right)^{2}-3^{2}}-\frac{62\sqrt{2}}{3-2\sqrt{10}}$$

4 मेळोवंक 2 चो 2 पॉवर मेजचो.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{4\left(\sqrt{10}\right)^{2}-3^{2}}-\frac{62\sqrt{2}}{3-2\sqrt{10}}$$

\sqrt{10} चो वर्ग 10 आसा.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{4\times 10-3^{2}}-\frac{62\sqrt{2}}{3-2\sqrt{10}}$$

40 मेळोवंक 4 आनी 10 गुणचें.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{40-3^{2}}-\frac{62\sqrt{2}}{3-2\sqrt{10}}$$

9 मेळोवंक 2 चो 3 पॉवर मेजचो.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{40-9}-\frac{62\sqrt{2}}{3-2\sqrt{10}}$$

31 मेळोवंक 40 आनी 9 वजा करचे.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}-\frac{62\sqrt{2}}{3-2\sqrt{10}}$$

न्युमरेटर आनी डिनोमिनेटर 3+2\sqrt{10} न गुणून \frac{62\sqrt{2}}{3-2\sqrt{10}} चो डिनोमिनेटर रेशनलायझ तर्कसंगत करचो.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}-\frac{62\sqrt{2}\left(3+2\sqrt{10}\right)}{\left(3-2\sqrt{10}\right)\left(3+2\sqrt{10}\right)}$$

विचारांत घेयात \left(3-2\sqrt{10}\right)\left(3+2\sqrt{10}\right). नेम वापरून गुणाकार विभिन्न चवकोनांत रुपांतरण करूं येताः \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}-\frac{62\sqrt{2}\left(3+2\sqrt{10}\right)}{3^{2}-\left(-2\sqrt{10}\right)^{2}}$$

9 मेळोवंक 2 चो 3 पॉवर मेजचो.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}-\frac{62\sqrt{2}\left(3+2\sqrt{10}\right)}{9-\left(-2\sqrt{10}\right)^{2}}$$

\left(-2\sqrt{10}\right)^{2} विस्तारीत करचो.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}-\frac{62\sqrt{2}\left(3+2\sqrt{10}\right)}{9-\left(-2\right)^{2}\left(\sqrt{10}\right)^{2}}$$

4 मेळोवंक 2 चो -2 पॉवर मेजचो.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}-\frac{62\sqrt{2}\left(3+2\sqrt{10}\right)}{9-4\left(\sqrt{10}\right)^{2}}$$

\sqrt{10} चो वर्ग 10 आसा.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}-\frac{62\sqrt{2}\left(3+2\sqrt{10}\right)}{9-4\times 10}$$

40 मेळोवंक 4 आनी 10 गुणचें.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}-\frac{62\sqrt{2}\left(3+2\sqrt{10}\right)}{9-40}$$

-31 मेळोवंक 9 आनी 40 वजा करचे.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}-\frac{62\sqrt{2}\left(3+2\sqrt{10}\right)}{-31}$$

-2\sqrt{2}\left(3+2\sqrt{10}\right) मेळोवंक 62\sqrt{2}\left(3+2\sqrt{10}\right) क -31 न भाग लावचो.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}-\left(-2\sqrt{2}\left(3+2\sqrt{10}\right)\right)$$

-2\sqrt{2}\left(3+2\sqrt{10}\right) च्या विरुध्दार्थी अंक 2\sqrt{2}\left(3+2\sqrt{10}\right) आसा.

$$\frac{\left(31\sqrt{2}+31\sqrt{5}\right)\left(2\sqrt{10}+3\right)}{31}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

31\sqrt{2}+31\sqrt{5}च्या प्रत्येकी टर्माक 2\sqrt{10}+3 च्या प्रत्येकी टर्मान गुणाकार करून वितरक गुणधर्म लागू करचो.

$$\frac{62\sqrt{10}\sqrt{2}+93\sqrt{2}+62\sqrt{5}\sqrt{10}+93\sqrt{5}}{31}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

10=2\times 5 गुणकपद काडचें. \sqrt{2}\sqrt{5} च्या वर्ग मूळाचो गुणाकार म्हूण \sqrt{2\times 5} च्या वर्गमूळाचो गुणाकार परत बरोवचो.

$$\frac{62\sqrt{2}\sqrt{5}\sqrt{2}+93\sqrt{2}+62\sqrt{5}\sqrt{10}+93\sqrt{5}}{31}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

2 मेळोवंक \sqrt{2} आनी \sqrt{2} गुणचें.

$$\frac{62\times 2\sqrt{5}+93\sqrt{2}+62\sqrt{5}\sqrt{10}+93\sqrt{5}}{31}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

124 मेळोवंक 62 आनी 2 गुणचें.

$$\frac{124\sqrt{5}+93\sqrt{2}+62\sqrt{5}\sqrt{10}+93\sqrt{5}}{31}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

10=5\times 2 गुणकपद काडचें. \sqrt{5}\sqrt{2} च्या वर्ग मूळाचो गुणाकार म्हूण \sqrt{5\times 2} च्या वर्गमूळाचो गुणाकार परत बरोवचो.

$$\frac{124\sqrt{5}+93\sqrt{2}+62\sqrt{5}\sqrt{5}\sqrt{2}+93\sqrt{5}}{31}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

5 मेळोवंक \sqrt{5} आनी \sqrt{5} गुणचें.

$$\frac{124\sqrt{5}+93\sqrt{2}+62\times 5\sqrt{2}+93\sqrt{5}}{31}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

310 मेळोवंक 62 आनी 5 गुणचें.

$$\frac{124\sqrt{5}+93\sqrt{2}+310\sqrt{2}+93\sqrt{5}}{31}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

403\sqrt{2} मेळोवंक 93\sqrt{2} आनी 310\sqrt{2} एकठांय करचें.

$$\frac{124\sqrt{5}+403\sqrt{2}+93\sqrt{5}}{31}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

217\sqrt{5} मेळोवंक 124\sqrt{5} आनी 93\sqrt{5} एकठांय करचें.

$$\frac{217\sqrt{5}+403\sqrt{2}}{31}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

7\sqrt{5}+13\sqrt{2} मेळोवंक 217\sqrt{5}+403\sqrt{2} च्या दरेक संज्ञेक 31 न भाग लावचो.

$$7\sqrt{5}+13\sqrt{2}+2\sqrt{2}\left(3+2\sqrt{10}\right)$$

3+2\sqrt{10} न 2\sqrt{2} गुणपाक विभाजक विशमाचो वापर करचो.

$$7\sqrt{5}+13\sqrt{2}+6\sqrt{2}+4\sqrt{10}\sqrt{2}$$

10=2\times 5 गुणकपद काडचें. \sqrt{2}\sqrt{5} च्या वर्ग मूळाचो गुणाकार म्हूण \sqrt{2\times 5} च्या वर्गमूळाचो गुणाकार परत बरोवचो.

$$7\sqrt{5}+13\sqrt{2}+6\sqrt{2}+4\sqrt{2}\sqrt{5}\sqrt{2}$$

2 मेळोवंक \sqrt{2} आनी \sqrt{2} गुणचें.

$$7\sqrt{5}+13\sqrt{2}+6\sqrt{2}+4\times 2\sqrt{5}$$

8 मेळोवंक 4 आनी 2 गुणचें.

$$7\sqrt{5}+13\sqrt{2}+6\sqrt{2}+8\sqrt{5}$$

19\sqrt{2} मेळोवंक 13\sqrt{2} आनी 6\sqrt{2} एकठांय करचें.

$$7\sqrt{5}+19\sqrt{2}+8\sqrt{5}$$

15\sqrt{5} मेळोवंक 7\sqrt{5} आनी 8\sqrt{5} एकठांय करचें.

$$15\sqrt{5}+19\sqrt{2}$$

गुणकपद

$$15 \sqrt{5} + 19 \sqrt{2} = 60.411077348$$