Rationalise the denominator of the following : (3√5 + √3) / (√5 - √3)
Solution:
Given, the expression is (3√5 + √3) / (√5 - √3)
We have to rationalise the denominator
To rationalise we have to take conjugate,
(3√5 + √3) / (√5 - √3) = (3√5 + √3) / (√5 - √3) × (√5 + √3) / (√5 + √3)
= (3√5 + √3)(√5 + √3) / (√5 + √3) / (√5 - √3)
By using algebraic identity,
(a² - b²) = (a - b)(a + b)
(√5 + √3)(√5 - √3) = (√5)² - (√3)²
= 5 - 3
= 2
So, (3√5 + √3)(√5 + √3) / (√5 + √3) / (√5 - √3) = (3√5 + √3)(√5 + √3) / 2
By multiplicative and distributive property,
(3√5 + √3)(√5 + √3) = 3√5(√5) + 3√5(√3) + √3(√5) + √3(√3)
= 3(5) + 3√15 + √15 + 3
= 15 + 3 + 3√15 + √15
= 18 + 4√15
Now, (3√5 + √3)(√5 + √3) / 2 = 18 + 4√15 / 2
= 2(9 + 2√15) / 2
= 9 + 2√15
Therefore, (3√5 + √3) / (√5 - √3) = 9 + 2√15
✦ Try This: Rationalise the denominator of the following : (3√2 + 2√3) / (√2 + √3)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 10(viii)
Rationalise the denominator of the following : (3√5 + √3) / (√5 - √3)
Summary:
Rationalizing is the process of multiplying a surd with another similar surd, to result in a rational number. On rationalising the denominator of (3√5 + √3) / (√5 - √3) we get 9 + 2√15
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