Question

2. Rationalise the denominator of (2 + sqrt(3))/(2 - sqrt(3))​

Answer 1

Answer:

7 + 4√3

Step-by-step explanation:

(2 + √3) / (2 - √3)

If the denominator is in the form of 'a + √b' then we should rationalize with 'a - √b'

If the denominator is in the form of 'a - √b' then we should  rationalize with  

'a + √b'

Rationalize the denominator by multiplying the numerator and denominator with (2 + √3) (as the denominator is 2 - √3)

⇒ (2 + √3) / (2 - √3)

= (2 + √3)*(2 + √3) / (2 - √3)*(2 + √3)

= (2 + √3)² / (2² - (√3)²)

= (2 + √3)² / (4 - 3)

= (2 + √3)²/1

= (2 + √3)²

= 2² + (√3)² + 2(2)(√3)   [∵(a+b)² = a² + b² + 2ab]

= 4 + 3 + 4√3

= 7 + 4√3