Question

Rationalize the following

1/8+3 root 5

Answer 1

Given : 1/(8 + 3√5)

To Find : Rationalize

Solution:

1/(8 + 3√5)

Rationalize by  multiplying numerator and denominator  with (8 - 3√5)

= {1/(8 + 3√5) } x {  (8 - 3√5) /  (8 - 3√5) }

=  (8 - 3√5) / (8 + 3√5) (8 - 3√5)

using (a + b)(a - b) = a² - b²

a = 8

b = 3√5

=  (8 - 3√5) / (8² -(3√5)²)

=  (8 - 3√5) / (64  - 45 )

= (8 - 3√5) /19

1/(8 + 3√5) = (8 - 3√5) /19

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