Question

Rationalize the denominators of the following:

 1 / (√5 + √2)

Answer 1

 1 / (√5 + √2)

We need to multiply the numerator and denominator of  1 / (√5 + √2) by √5 - √2, to get

 1 / (√5 + √2) x (√5 - √2) / (√5 - √2) 

= (√5 - √2) / (√5 + √2) (√5 - √2)

We need to apply the formula (a - b)(a +b) = a² -b² int the denominator to get

1 / (√5 + √2) = (√5 - √2) / (√5)² -(√2)²

= (√5 - √2) / (5 - 2)

= (√5 - √2) / 3

Therefore, we conclude that on rationalizing the denominator of 1 / (√5 + √2),we get (√5 - √2) / 3.