# Rationalize the denominators of the following: 1 / (√5 + √2)

156 views

Rationalize the denominators of the following:

1 / (√5 + √2)

by (24.8k points)
selected

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.