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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