सोडोवचें frac{(sqrt{5}-sqrt{2})(3sqrt{5}+sqrt{2})}{3sqrt{5}+2sqrt{2}}

$$\frac { ( \sqrt { 5 } - \sqrt { 2 } ) ( 3 \sqrt { 5 } + \sqrt { 2 } ) } { 3 \sqrt { 5 } + 2 \sqrt { 2 } }$$

मूल्यांकन करचें

$$\frac{47\sqrt{5}-56\sqrt{2}}{37}\approx 0.699979336$$

सोडोवणी पांवडे

न्युमरेटर आनी डिनोमिनेटर 3\sqrt{5}-2\sqrt{2} न गुणून \frac{\left(\sqrt{5}-\sqrt{2}\right)\left(3\sqrt{5}+\sqrt{2}\right)}{3\sqrt{5}+2\sqrt{2}} चो डिनोमिनेटर रेशनलायझ तर्कसंगत करचो.

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

विचारांत घेयात \left(3\sqrt{5}+2\sqrt{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right). नेम वापरून गुणाकार विभिन्न चवकोनांत रुपांतरण करूं येताः \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\left(3\sqrt{5}\right)^{2} विस्तारीत करचो.

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

9 मेळोवंक 2 चो 3 पॉवर मेजचो.

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

\sqrt{5} चो वर्ग 5 आसा.

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

45 मेळोवंक 9 आनी 5 गुणचें.

$$\frac{\left(\sqrt{5}-\sqrt{2}\right)\left(3\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{45-\left(2\sqrt{2}\right)^{2}}$$

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

$$\frac{\left(\sqrt{5}-\sqrt{2}\right)\left(3\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{45-2^{2}\left(\sqrt{2}\right)^{2}}$$

4 मेळोवंक 2 चो 2 पॉवर मेजचो.

$$\frac{\left(\sqrt{5}-\sqrt{2}\right)\left(3\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{45-4\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} चो वर्ग 2 आसा.

$$\frac{\left(\sqrt{5}-\sqrt{2}\right)\left(3\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{45-4\times 2}$$

8 मेळोवंक 4 आनी 2 गुणचें.

$$\frac{\left(\sqrt{5}-\sqrt{2}\right)\left(3\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{45-8}$$

37 मेळोवंक 45 आनी 8 वजा करचे.

$$\frac{\left(\sqrt{5}-\sqrt{2}\right)\left(3\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{37}$$

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

$$\frac{\left(3\left(\sqrt{5}\right)^{2}+\sqrt{5}\sqrt{2}-3\sqrt{2}\sqrt{5}-\left(\sqrt{2}\right)^{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{37}$$

\sqrt{5} चो वर्ग 5 आसा.

$$\frac{\left(3\times 5+\sqrt{5}\sqrt{2}-3\sqrt{2}\sqrt{5}-\left(\sqrt{2}\right)^{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{37}$$

15 मेळोवंक 3 आनी 5 गुणचें.

$$\frac{\left(15+\sqrt{5}\sqrt{2}-3\sqrt{2}\sqrt{5}-\left(\sqrt{2}\right)^{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{37}$$

\sqrt{5} आनी \sqrt{2} गुणूंक, वर्गमुळाच्या खाला संख्या गुणची.

$$\frac{\left(15+\sqrt{10}-3\sqrt{2}\sqrt{5}-\left(\sqrt{2}\right)^{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{37}$$

\sqrt{2} आनी \sqrt{5} गुणूंक, वर्गमुळाच्या खाला संख्या गुणची.

$$\frac{\left(15+\sqrt{10}-3\sqrt{10}-\left(\sqrt{2}\right)^{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{37}$$

-2\sqrt{10} मेळोवंक \sqrt{10} आनी -3\sqrt{10} एकठांय करचें.

$$\frac{\left(15-2\sqrt{10}-\left(\sqrt{2}\right)^{2}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{37}$$

\sqrt{2} चो वर्ग 2 आसा.

$$\frac{\left(15-2\sqrt{10}-2\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{37}$$

13 मेळोवंक 15 आनी 2 वजा करचे.

$$\frac{\left(13-2\sqrt{10}\right)\left(3\sqrt{5}-2\sqrt{2}\right)}{37}$$

13-2\sqrt{10}च्या प्रत्येकी टर्माक 3\sqrt{5}-2\sqrt{2} च्या प्रत्येकी टर्मान गुणाकार करून वितरक गुणधर्म लागू करचो.

$$\frac{39\sqrt{5}-26\sqrt{2}-6\sqrt{10}\sqrt{5}+4\sqrt{2}\sqrt{10}}{37}$$

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

$$\frac{39\sqrt{5}-26\sqrt{2}-6\sqrt{5}\sqrt{2}\sqrt{5}+4\sqrt{2}\sqrt{10}}{37}$$

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

$$\frac{39\sqrt{5}-26\sqrt{2}-6\times 5\sqrt{2}+4\sqrt{2}\sqrt{10}}{37}$$

-30 मेळोवंक -6 आनी 5 गुणचें.

$$\frac{39\sqrt{5}-26\sqrt{2}-30\sqrt{2}+4\sqrt{2}\sqrt{10}}{37}$$

-56\sqrt{2} मेळोवंक -26\sqrt{2} आनी -30\sqrt{2} एकठांय करचें.

$$\frac{39\sqrt{5}-56\sqrt{2}+4\sqrt{2}\sqrt{10}}{37}$$

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

$$\frac{39\sqrt{5}-56\sqrt{2}+4\sqrt{2}\sqrt{2}\sqrt{5}}{37}$$

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

$$\frac{39\sqrt{5}-56\sqrt{2}+4\times 2\sqrt{5}}{37}$$

8 मेळोवंक 4 आनी 2 गुणचें.

$$\frac{39\sqrt{5}-56\sqrt{2}+8\sqrt{5}}{37}$$

47\sqrt{5} मेळोवंक 39\sqrt{5} आनी 8\sqrt{5} एकठांय करचें.

$$\frac{47\sqrt{5}-56\sqrt{2}}{37}$$