Question

Plz answer this question​

Answer 1

Answer:

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Answer 2

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

$\longrightarrow\sf{\displaystyle\sqrt{\frac{-\sqrt{3}+2}{\sqrt{3}+2}}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{-\sqrt{3}+2}}{\sqrt{\sqrt{3}+2}}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{-\sqrt{3}+2} \cdot \sqrt{\sqrt{3}+2}}{\sqrt{\sqrt{3}+2} \cdot \sqrt{\sqrt{3}+2}}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{(-\sqrt{3}+2)(\sqrt{3}+2)}}{\sqrt{(\sqrt{3}+2)(\sqrt{3}+2)}}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{-\sqrt{3} \cdot \sqrt{3}-\sqrt{3} \cdot 2+2 \cdot \sqrt{3}+2 \cdot 2}}{\sqrt{(\sqrt{3}+2)^{1+1}}}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{-\sqrt{3 \cdot 3}-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}+4}}{\sqrt{(\sqrt{3}+2)^{2}}}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{-\sqrt{3^{1+1}}-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}+4}}{(\sqrt{3}+2)^{\frac{2}{2}}}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{-\sqrt{3^{2}}-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}+4}}{\sqrt{3}+2}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{-3^{\frac{2}{2}}-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}+4}}{\sqrt{3}+2}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{-3-2 \cdot \sqrt{3}}+2 \cdot \sqrt{3}+4}{\sqrt{3}+2}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}-3+4}}{\sqrt{3}+2}}$

$\longrightarrow\sf{\displaystyle\frac{1}{\sqrt{3}+2}}$

$\longrightarrow\sf{\displaystyle \frac{\sqrt{3}-2}{(\sqrt{3}+2)(\sqrt{3}-2)}}$

$\longrightarrow\sf{\displaystyle \frac{\sqrt{3}-2}{\sqrt{3} \cdot \sqrt{3}-\sqrt{3} \cdot 2+2 \cdot \sqrt{3}-2 \cdot 2}}$

$\longrightarrow\sf{\displaystyle \frac{\sqrt{3}-2}{\sqrt{3 \cdot 3}-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}-4}}$

$\longrightarrow\sf{\displaystyle \frac{\sqrt{3}-2}{\sqrt{3^{1+1}}-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}-4}}$

$\longrightarrow\sf{\displaystyle \frac{\sqrt{3}-2}{\sqrt{3^{2}}-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}-4}}$

$\longrightarrow\sf{\displaystyle\frac{\sqrt{3}-2}{3^{\frac{2}{2}}-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}-4}}$

$\longrightarrow\sf{\displaystyle \frac{\sqrt{3}-2}{3-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}-4}}$

$\longrightarrow\sf{\displaystyle \frac{\sqrt{3}-2}{-2 \cdot \sqrt{3}+2 \cdot \sqrt{3}+3-4}}$

$\longrightarrow\sf{\displaystyle \frac{\sqrt{3}-2}{3-4}}$

$\longrightarrow\sf{\displaystyle \frac{\sqrt{3}-2}{-1}}$

$\longrightarrow\sf{\displaystyle- \frac{\sqrt{3}-2}{1}}$

$\longrightarrow\sf{-(\sqrt{3}-2)}$

➤ Substitute the value of  $\sf{\sqrt{3}}$

• As it is Given $\sf{\sqrt{3}}$ = 1.732

$\longrightarrow\sf{-(1.732-2)}$

$\longrightarrow\sf{-(-0.268)}$

$\large\boxed{\boxed{\longrightarrow\sf{0.268}}}$