सोडोवचें 5/2sqrt{7-2sqrt{5}}

$$\frac { 5 } { 2 \sqrt { 7 } - 2 \sqrt { 5 } }$$

मूल्यांकन करचें

$$\frac{5\left(\sqrt{5}+\sqrt{7}\right)}{4}\approx 6.102274111$$

सोडोवणी पांवडे

न्युमरेटर आनी डिनोमिनेटर 2\sqrt{7}+2\sqrt{5} न गुणून \frac{5}{2\sqrt{7}-2\sqrt{5}} चो डिनोमिनेटर रेशनलायझ तर्कसंगत करचो.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{\left(2\sqrt{7}-2\sqrt{5}\right)\left(2\sqrt{7}+2\sqrt{5}\right)}$$

विचारांत घेयात \left(2\sqrt{7}-2\sqrt{5}\right)\left(2\sqrt{7}+2\sqrt{5}\right). नेम वापरून गुणाकार विभिन्न चवकोनांत रुपांतरण करूं येताः \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{\left(2\sqrt{7}\right)^{2}-\left(-2\sqrt{5}\right)^{2}}$$

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

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{2^{2}\left(\sqrt{7}\right)^{2}-\left(-2\sqrt{5}\right)^{2}}$$

4 मेळोवंक 2 चो 2 पॉवर मेजचो.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{4\left(\sqrt{7}\right)^{2}-\left(-2\sqrt{5}\right)^{2}}$$

\sqrt{7} चो वर्ग 7 आसा.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{4\times 7-\left(-2\sqrt{5}\right)^{2}}$$

28 मेळोवंक 4 आनी 7 गुणचें.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-\left(-2\sqrt{5}\right)^{2}}$$

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

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-\left(-2\right)^{2}\left(\sqrt{5}\right)^{2}}$$

4 मेळोवंक 2 चो -2 पॉवर मेजचो.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-4\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} चो वर्ग 5 आसा.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-4\times 5}$$

20 मेळोवंक 4 आनी 5 गुणचें.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{28-20}$$

8 मेळोवंक 28 आनी 20 वजा करचे.

$$\frac{5\left(2\sqrt{7}+2\sqrt{5}\right)}{8}$$

2\sqrt{7}+2\sqrt{5} न 5 गुणपाक विभाजक विशमाचो वापर करचो.

$$\frac{10\sqrt{7}+10\sqrt{5}}{8}$$