सोडोवचें frac{2+sqrt{3}}{3sqrt{2}+2sqrt{7}}

$$\frac { 2 + \sqrt { 3 } } { 3 \sqrt { 2 } + 2 \sqrt { 7 } }$$

मूल्यांकन करचें

$$\frac{\sqrt{21}}{5}+\frac{2\sqrt{7}}{5}-\frac{3\sqrt{2}}{5}-\frac{3\sqrt{6}}{10}\approx 0.391440603$$

सोडोवणी पांवडे

न्युमरेटर आनी डिनोमिनेटर 3\sqrt{2}-2\sqrt{7} न गुणून \frac{2+\sqrt{3}}{3\sqrt{2}+2\sqrt{7}} चो डिनोमिनेटर रेशनलायझ तर्कसंगत करचो.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{\left(3\sqrt{2}+2\sqrt{7}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}$$

विचारांत घेयात \left(3\sqrt{2}+2\sqrt{7}\right)\left(3\sqrt{2}-2\sqrt{7}\right). नेम वापरून गुणाकार विभिन्न चवकोनांत रुपांतरण करूं येताः \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{7}\right)^{2}}$$

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

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{3^{2}\left(\sqrt{2}\right)^{2}-\left(2\sqrt{7}\right)^{2}}$$

9 मेळोवंक 2 चो 3 पॉवर मेजचो.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{9\left(\sqrt{2}\right)^{2}-\left(2\sqrt{7}\right)^{2}}$$

\sqrt{2} चो वर्ग 2 आसा.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{9\times 2-\left(2\sqrt{7}\right)^{2}}$$

18 मेळोवंक 9 आनी 2 गुणचें.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-\left(2\sqrt{7}\right)^{2}}$$

\left(2\sqrt{7}\right)^{2} विस्तारीत करचो.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-2^{2}\left(\sqrt{7}\right)^{2}}$$

4 मेळोवंक 2 चो 2 पॉवर मेजचो.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-4\left(\sqrt{7}\right)^{2}}$$

\sqrt{7} चो वर्ग 7 आसा.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-4\times 7}$$

28 मेळोवंक 4 आनी 7 गुणचें.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{18-28}$$

-10 मेळोवंक 18 आनी 28 वजा करचे.

$$\frac{\left(2+\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{7}\right)}{-10}$$

2+\sqrt{3}च्या प्रत्येकी टर्माक 3\sqrt{2}-2\sqrt{7} च्या प्रत्येकी टर्मान गुणाकार करून वितरक गुणधर्म लागू करचो.

$$\frac{6\sqrt{2}-4\sqrt{7}+3\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{7}}{-10}$$

\sqrt{3} आनी \sqrt{2} गुणूंक, वर्गमुळाच्या खाला संख्या गुणची.

$$\frac{6\sqrt{2}-4\sqrt{7}+3\sqrt{6}-2\sqrt{3}\sqrt{7}}{-10}$$

\sqrt{3} आनी \sqrt{7} गुणूंक, वर्गमुळाच्या खाला संख्या गुणची.

$$\frac{6\sqrt{2}-4\sqrt{7}+3\sqrt{6}-2\sqrt{21}}{-10}$$

न्युमरेटर आनी डिनोमिनेटर -1 वरवीं गुणचो.

$$\frac{-6\sqrt{2}+4\sqrt{7}-3\sqrt{6}+2\sqrt{21}}{10}$$