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# If √2 = 1.4142, then √[(√2 - 1)/(√2 + 1)] is equal to

a. 2.4142

b. 5.8282

c. 0.4142

d. 0.1718

**Solution:**

Given

√2 = 1.4142

\(\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}\)

Let us multiply both __numerator__ and __denominator__ by √2 -1

= \(\sqrt{\frac{(\sqrt{2}-1)(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}}\)

Using the algebraic identity (a + b) (a - b) = a² - b²

= \(\sqrt{\frac{(\sqrt{2}-1)^{2}}{(\sqrt{2})^{2}-(1)^{2}}}\)

By further calculation

= \(\sqrt{\frac{(\sqrt{2}-1)^{2}}{2 - 1}}\)

= \(\sqrt{\frac{(\sqrt{2}-1)^{2}}{1}}\)

So we get

= √2 - 1

Let us substitute the value of √2

= 1.4142 - 1

= 0.4142

Therefore, √[(√2 - 1)/(√2 + 1)] is equal to 0.4142.

**✦ Try This: **If √3 = 1.7320, the \(\sqrt{\frac{\sqrt{3}-1}{\sqrt{3}+1}}\) is equal to

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 1

**NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 16**

## If √√2 = 1.4142, then √[(√2 - 1)/(√2 + 1)] is equal to a. 2.4142, b. 5.8282, c. 0.4142, d. 0.1718

**Summary**:

Rationalizing the denominator means the process of moving a root, for instance, a cube root or a square root from the bottom of a fraction (denominator) to the top of the fraction (numerator). If √2 = 1.4142, then √[(√2 - 1)/(√2 + 1)] is equal to 0.4142

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