Rationalise the denominator of the following: √6 / (√2 + √3)
Solution:
Given, the expression is √6 / (√2 + √3)
We have to rationalise the denominator
To rationalise we have to take conjugate,
√6 / (√2 + √3) = √6 / (√2 + √3) × (√2 - √3) / (√2 - √3)
= √6(√2 - √3) / (√2 + √3)(√2 - √3)
By using algebraic identity,
(a² - b²) = (a - b)(a + b)
(√2 + √3)(√2 - √3) = (√2)² - (√3)²
= 2 - 3
= -1
Now, √6(√2 - √3) / (√2 + √3)(√2 - √3) = √6(√2 - √3) / (-1)
= √6(√3 - √2)
By multiplicative and distributive property,
√6(√3 - √2) = √6×√3 - √6×√2
= √18 - √12
Therefore, √6 / (√2 + √3) = √18 - √12
✦ Try This: Rationalise the denominator of the following: √7 / (√2 + √5)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 10(vi)
Rationalise the denominator of the following: √6 / (√2 + √3)
Summary:
A conjugate is a similar surd but with a different sign. On rationalising the denominator of √6 / (√2 + √3) we get √18 - √12
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