Question

If \[\sqrt{2} = 1 . 4142\] then \[\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}}\] is equal to

पर्याय

• 0.1718

•  5.8282

•  0.4142

• 2.4142

Answer 1

 0.4142

Explanation:

Given that `sqrt2= 1.4142`, we need to find the value of `sqrt((sqrt2-1)/(sqrt2+1))`

We can rationalize the denominator of the given expression. We know that rationalization factor for  `sqrt2+1` is`sqrt2-1`. We will multiply numerator and denominator of the given expression `sqrt((sqrt2-1)/(sqrt2+1))`by`sqrt2-1`, to get

`sqrt((sqrt2-1)/(sqrt2+1)) = sqrt((sqrt2-1)/(sqrt2+1)xxsqrt((sqrt2-1)/(sqrt2-1)))`

` = sqrt((sqrt2-1)^2/((sqrt2)^2-1))`

` = sqrt((sqrt2-1)^2)/(sqrt((sqrt2)^2-1))`

\[\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}} = \frac{\sqrt{2} - 1}{1}\]

Putting the value of `sqrt2`, we get 

`sqrt2 -1 = 4.4142 - 1`

`= 0.4142`