सोडोवचें 14/5sqrt{3-sqrt{5}}

$$\frac{ 14 }{ 5 \sqrt{ 3 } - \sqrt{ 5 } }$$

मूल्यांकन करचें

$$\frac{\sqrt{5}\left(\sqrt{15}+1\right)}{5}\approx 2.179264403$$

सोडोवणी पांवडे

न्युमरेटर आनी डिनोमिनेटर 5\sqrt{3}+\sqrt{5} न गुणून \frac{14}{5\sqrt{3}-\sqrt{5}} चो डिनोमिनेटर रेशनलायझ तर्कसंगत करचो.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{\left(5\sqrt{3}-\sqrt{5}\right)\left(5\sqrt{3}+\sqrt{5}\right)}$$

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

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{\left(5\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

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

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{5^{2}\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

25 मेळोवंक 2 चो 5 पॉवर मेजचो.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{25\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$

\sqrt{3} चो वर्ग 3 आसा.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{25\times 3-\left(\sqrt{5}\right)^{2}}$$

75 मेळोवंक 25 आनी 3 गुणचें.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{75-\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} चो वर्ग 5 आसा.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{75-5}$$

70 मेळोवंक 75 आनी 5 वजा करचे.

$$\frac{14\left(5\sqrt{3}+\sqrt{5}\right)}{70}$$

\frac{1}{5}\left(5\sqrt{3}+\sqrt{5}\right) मेळोवंक 14\left(5\sqrt{3}+\sqrt{5}\right) क 70 न भाग लावचो.

$$\frac{1}{5}\left(5\sqrt{3}+\sqrt{5}\right)$$

5\sqrt{3}+\sqrt{5} न \frac{1}{5} गुणपाक विभाजक विशमाचो वापर करचो.

$$\frac{1}{5}\times 5\sqrt{3}+\frac{1}{5}\sqrt{5}$$

5 आनी 5 रद्द करचें.

$$\sqrt{3}+\frac{1}{5}\sqrt{5}$$