Rationalise the denominator of the following: (√3 + √2) / (√3 - √2)
Solution:
Given, the expression is (√3 + √2) / (√3 - √2)
We have to rationalise the denominator
To rationalise we have to take conjugate,
(√3 + √2) / (√3 - √2) = (√3 + √2) / (√3 - √2) × (√3 + √2) / (√3 + √2)
= (√3 + √2)(√3 + √2) / (√3 + √2)(√3 - √2)
= (√3 + √2)² / (√3 + √2)(√3 - √2)
By using algebraic identity,
(a² - b²) = (a - b)(a + b)
(√3 + √2)(√3 - √2) = (√3)² - (√2)²
= 3 - 2
= 1
So, (√3 + √2)² / (√3 + √2)(√3 - √2) = (√3 + √2)² / (1)
= (√3 + √2)²
By using algebraic identity,
(a + b)² = a² + 2ab + b²
So, (√3 + √2)² = (√3)² + 2(√3)(√2) + (√2)²
= 3 + 2√6 + 2
= 5 + 2√6
Therefore, (√3 + √2) / (√3 - √2) = 5 + 2√6
✦ Try This: Rationalise the denominator of the following : (√3 + √5) / (√5 - √3)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 10(vii)
Rationalise the denominator of the following: (√3 + √2) / (√3 - √2)
Summary:
In the process of rationalizing a denominator, the conjugate is the rationalizing factor. On rationalising the denominator of (√3 + √2) / (√3 - √2) we get 5 + 2√6
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