Question

rationalize the denominator 1 upon root 5 minus root 3

Answer 1

Hola

Answer -

1/√5 - √3

1/√5 - √3 × (√5 + √3) / (√5 + √3)

= (√5 + √3)/(√5)² - (√3)²

as, (a + b) (a - b) = a² - b²

Therefore,

(√5 + √3)/5 - 3

= (√5 + √3)/2

Hope it helps!

Answer 2

Concept

Rationalisation is a method to eliminate the irrational number present in the denominator.

Find

Rationalise 1 / ( √5 - √3 )

Solution

1 / ( √5 - √3 )

Multiply both numerator and denominator with ( √5 + √3 )

[1*( √5 + √3 )] / [( √5 + √3 )*( √5 - √3 )]

Using (a+b)(a-b) = a² - b²

( √5 + √3 ) / [(√5)² - (√3)²]

( √5 + √3 ) / (5 - 3)

( √5 + √3 ) / 2

After rationalising of 1 / ( √5 - √3 ) we get ( √5 + √3 ) / 2

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