# If √ 2 = 1 . 4142 Then √ √ 2 − 1 √ 2 + 1 is Equal to - Mathematics

MCQ

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

• 0.1718

•  5.8282

•  0.4142

• 2.4142

#### Solution

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 issqrt2-1. We will multiply numerator and denominator of the given expression sqrt((sqrt2-1)/(sqrt2+1))bysqrt2-1, 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

Concept: Laws of Exponents for Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.4 | Q 21 | Page 18

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