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

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

मूल्यांकन करचें

$$\frac{7-2\sqrt{6}}{5}\approx 0.420204103$$

सोडोवणी पांवडे

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

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

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

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

\left(2\sqrt{3}-\sqrt{2}\right)^{2} मेळोवंक 2\sqrt{3}-\sqrt{2} आनी 2\sqrt{3}-\sqrt{2} गुणचें.

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

बायनोमियल प्रमेयाचो वापर करून \left(a-b\right)^{2}=a^{2}-2ab+b^{2} विस्तारावचें \left(2\sqrt{3}-\sqrt{2}\right)^{2}.

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

\sqrt{3} चो वर्ग 3 आसा.

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

12 मेळोवंक 4 आनी 3 गुणचें.

$$\frac{12-4\sqrt{3}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{\left(2\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{12-4\sqrt{6}+\left(\sqrt{2}\right)^{2}}{\left(2\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} चो वर्ग 2 आसा.

$$\frac{12-4\sqrt{6}+2}{\left(2\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

14 मेळोवंक 12 आनी 2 ची बेरीज करची.

$$\frac{14-4\sqrt{6}}{\left(2\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{14-4\sqrt{6}}{2^{2}\left(\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

4 मेळोवंक 2 चो 2 पॉवर मेजचो.

$$\frac{14-4\sqrt{6}}{4\left(\sqrt{3}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$

\sqrt{3} चो वर्ग 3 आसा.

$$\frac{14-4\sqrt{6}}{4\times 3-\left(\sqrt{2}\right)^{2}}$$

12 मेळोवंक 4 आनी 3 गुणचें.

$$\frac{14-4\sqrt{6}}{12-\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} चो वर्ग 2 आसा.

$$\frac{14-4\sqrt{6}}{12-2}$$

10 मेळोवंक 12 आनी 2 वजा करचे.

$$\frac{14-4\sqrt{6}}{10}$$

गुणकपद

$$\frac{7 - 2 \sqrt{6}}{5} = 0.4202041028867288$$