Question

If√2=1.4142,then √{(√2-1)÷(√2+1)}

Answer 1

In order to get answer easily, we will rationalize it first.

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

To rationalize, we will multiply with (√2 - 1) on both numerator and denominator.

=>
$\frac{( \sqrt{2} - 1)( \sqrt{2} - 1) }{( \sqrt{2} + 1)( \sqrt{2} - 1) } \\ \\ = > \frac{( \sqrt{2} - 1) {}^{2} }{( \sqrt{2) {}^{2} } - (1) {}^{2} } \\ \\ = > \frac{2 + 1 - 2 \sqrt{2} }{2 - 1} \\ \\ = 3 - 2 \sqrt{2}$


So, {√2 - 1} ÷ {√2 + 1} = 3 - 2√2

Now put the value of √2

=> 3 - 2(1.4142)

= 3 - 2.8284

= 0.1716


Hope it helps dear friend ☺️