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

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

मूल्यांकन करचें

$$\frac{\sqrt{2}+\sqrt{6}-2\sqrt{3}-1}{5}\approx -0.120079662$$

सोडोवणी पांवडे

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

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

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

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

\sqrt{2} चो वर्ग 2 आसा.

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

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

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

4 मेळोवंक 2 चो 2 पॉवर मेजचो.

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

\sqrt{3} चो वर्ग 3 आसा.

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

12 मेळोवंक 4 आनी 3 गुणचें.

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

-10 मेळोवंक 2 आनी 12 वजा करचे.

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

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

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

\sqrt{2} चो वर्ग 2 आसा.

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

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

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