Respuesta :

Answer :

  • (5√2 + 2√5 - 5 - √10)/3

Explanation:

A rational number is the one which can be written in the form of p/q ,where q ≠0.

In order to rationalize the denominator,we are required to follow these steps

1) find the conjugate of the denominator.

2) multiply it by both the numerator and the denominator

3) simplify

the conjugate of the denominator √5 - √2 is √5 + √2

thus, (√10 - √5)/ (√5 - √2 ) =

  • ((√10 - √5)(√5 + √2))/((√5 - √2)(√5 + √2))
  • (√10*√5 + √10*√2 - √5*√5 - √5*√2)/(√5*√5 - √5*√2 +√5*√2 - √2*√2)
  • (√50 + √20- 5 - √10)/(5 - 2)
  • (5√2 + 2√5 - 5 - √10)/3

therefore, the rationalized denominator version of (√10 - √5) / (√5 - √2) is (5√2 + 2√5 - 5 - √10)/3 .