Question

Rationalise the denominator ...1) 1 by root 7 -root 6​

Answer 1

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Answer 2

Step-by-step explanation:

Solution:

1/(√7 - √6)

The denominator is √7 - √6.

We know that

Rationalising factor of √a - √b = √a + √b.

So, the rationalising factor of √7 - √6 = √7 + √6.

On comparing the denominator them

=> [1/(√7 - √6)]×[(√7 - √6)/(√7- √6)]

=> [1(√7 + √6)]/[(√7 - √6)(√7 + √6)]

Applying algebraic identity in denominator; (a-b)(a+b) = a^2 - b^2. Where, a = √7 and b = √6.

=> [1(√7 + √6)]/[(√7)^2 - (√6)^2)]

=> [1(√7 + √6)]/(7 - 6)

=> [1(√7 + √6)]/1

=> 1(√7 + √6)

=> √7 + √6

Hence, the denominator is rationalised.

Answer:

→ √7 - √6

Used Formulae:

• Rationalising factor of √a - √b = √a + √b.

• (a-b)(a+b) = a^2 - b^2.