Question

solve this question ​

Answer 1

Answer:

Given

$\sqrt{ \frac{ \sqrt{2} + 1}{ \sqrt{2} - 1 } }$

We have to use

$\sqrt{2} = 1.4142$

Now

$\sqrt{ \frac{ \sqrt{2} + 1}{ \sqrt{2} - 1} } \\ = \sqrt{ \frac{ \sqrt{2} + 1 }{ \sqrt{2} - 1 } \times \frac{ \sqrt{2} + 1 }{ \sqrt{2} + 1 } } \\ = \sqrt{ \frac{( \sqrt{2} + 1) {}^{2} }{( \sqrt{2}) {}^{2} - 1 {}^{2} } } \\ \sqrt{ \frac{( \sqrt{2} + 1) {}^{2} }{(2 - 1)} } \\ = \sqrt{ \frac{( \sqrt{2} + 1) {}^{2} }{1} } \\ \sqrt{( \sqrt{2} + 1) {}^{2} } \\ = ( \sqrt{2} + 1) {}^{2 \times \frac{1}{2} } \\ = \sqrt{2} + 1 \\ = 1.4142 + 1 \\ = 2.4142$