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Rationalise the denominator of the following: 16/(√41 - 5)

Solution:

Given, the expression is 16/(√41 - 5)

We have to rationalise the denominator.

To rationalise we have to take conjugate,

16/(√41 - 5) = 16/(√41 - 5) × (√41 + 5)/(√41 + 5)

= 16(√41 + 5) / (√41 - 5)(√41 + 5)

By using algebraic identity,

(a² - b²) = (a - b)(a + b)

So, (√41 - 5)(√41 + 5) = (√41)² - (5)²

= 41 - 25

= 16

Now, 16(√41 + 5) / (√41 - 5)(√41 + 5) = 16(√41 + 5) / 16

= √41 + 5

Therefore, 16/(√41 - 5) = √41 + 5

✦ Try This: Rationalise the denominator of the following: 16 / (√41 - 5)

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

NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 10(iv)

Rationalise the denominator of the following: 16/(√41 - 5)

Summary:

Rationalizing is the process of multiplying a surd with another similar surd, to result in a rational number. On rationalising the denominator of 16/(√41 - 5) we get √41 + 5

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