Question

3. Rationalise the denominator.
1÷root 7 - root 6​

Answer 1

Equation Given: 1/√7-√6

Now, to rationalize the denominator, we multiply the equation with its opposite

1/(√7-√6) × 1/(√7+√6)

= 1/(√7)^2-(√6)^2. {Using a^2-b^2=(a+b)(a-b)}

= 1/7-6

= 1/1

= 1

Hence, the answer is 1. Hope this helps! Please mark it as brainliest.

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. of

Answer:

→ √7 - √6

Used Formulae:

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

• (a-b)(a+b) = a^2 - b^2.