Rationalise the denominator of the following: (2 + √3)/(2 - √3)
Solution:
Given, the expression is (2 + √3)/(2 - √3)
We have to rationalise the denominator
To rationalise we have to take conjugate,
(2 + √3)/(2 - √3) = (2 + √3)/(2 - √3) × (2 + √3)/(2 + √3)
= (2 + √3)² / (2 + √3)\(2 - √3)
By using algebraic identity,
(a² - b²) = (a - b)(a + b)
(2 + √3)(2 - √3) = (2)² - (√3)²
= 4 - 3
= 1
So, (2 + √3)² / (2 + √3)(2 - √3) = (2 + √3)² / (1)
= (2 + √3)²
By using algebraic identity,
(a + b)² = a² + 2ab + b²
So, (2 + √3)² = (2)² + 2(2)(√3) + (√3)²
= 4 + 4√3 + 3
= 7 + 4√3
Therefore, (2 + √3)/(2 - √3) = 7 + 4√3
✦ Try This: Rationalise the denominator of the following: (4 + √3)/(4 - √3)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 10(v)
Rationalise the denominator of the following: (2 + √3)/(2 - √3)
Summary:
The surd that is used to multiply is called the rationalizing factor (RF). On rationalising the denominator of (2 + √3)/(2 - √3) we get 7 + 4√3
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