Question

rationalise the denominator of the following ​

Answer 1

Answer:

18/4-√17=18/4-√17*√17/√17

18√17/4√17-17

Answer 2

Step-by-step explanation:

Given:-

18/(4 - √7)

To find:-

Rationalising the denominator.

Solution:-

Given expression,

18/(4 - √7)

The denominator is 4 - √7.

We know that

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

So, the rationalising factor of 4 - √7 = 4 + √7.

On rationalising the denominator them.

→ [18/(4 - √7)] × [(4 + √7)/(4 + √7)]

→ [18(4 + √7)]/[(4 - √7)(4 + √7)]

• In denominator applying algebraic identity because it is in the form of (a - b)(a + b) = a^2 - b^2. Where, we have to put in our expression a = 4 and b = √7.

→ [18(4 + √7)]/[(4)^2 - (√7)^2]

→ [18(4 + √7)]/(16 - 7)

→ [18(4+ √7)]/9

• Cancel 9(denominator) two times from 18(numerator).
• To get 2.

→ 2(4 + √7)

Hence, the denominator is rationalised.

Answer:-

2(4 + √7)

Used Formulae:-

(a - b)(a + b) = a^2 - b^2

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