Question

If √2=1.414, find the value of 1/√2+1

Answer 1

   (1/ √2 + 1 ) * ( √2 - 1 / √2 - 1 ) 
= √2 - 1/(√2)² - ( 1 )²
= √2 - 1 / 2-1
= √2 -1 / 1
= √2 - 1
= 1.414 - 1
= 0.414

Answer 2

Answer:

$\frac{1}{\sqrt{2}+1}=0.414$

Step-by-step explanation:

Given : $\sqrt{2}=1.414$

To Find :$\frac{1}{\sqrt{2}+1}$

Solution :

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

Rationalize

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

Identity : $(a+b)(a-b)a^2-b^2$

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

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

$1.414-1$

$0.414$

Hence $\frac{1}{\sqrt{2}+1}=0.414$