Question

Rationalize the denominator of the fraction √5 /(√8 - √3)

Answer 1

Answer is 2/5 (√10 + √15)

Explanation:

• Step 1: To rationalize the denominator, multiply numerator and denominator by the conjugate of the denominator = (√8 + √3)

√5 (√8 + √3)/(√8 - √3)(√8 + √3) = (√40 + √15)/(8 - 3)

[using the identity (a+b)(a-b) = a² - b²]

= 2/5 (√10 + √15)

Answer 2

`(2√(10)+√(15) )/(5)`

Explanation:

`(√(5) )/(√(8)-√(3) ) =(√(5)*(√(8)+√(3)) )/((√(8)-√(3))(√(8)+√(3)) ) =(√(40)+√(15) )/(8-3) =(2√(10)+√(15) )/(5)`