Question

Rationalize the denominators of the following:

1 / (√7 - 2)

Answer 1

1/(√7 - 2)

We need to multiply the numerator and denominator of 1/(√7 - 2) by √7 + 2, to get

1/(√7 - 2) x (√7 + 2)/(√7 + 2) 

= (√7 + 2)/(√7 - 2)(√7 + 2)

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

1/(√7 - 2) = (√7 + 2)/(√7)² - (2)²

= (√7 + 2)/(7 -4)

= (√7 + 2)/3

Therefore, we conclude that on rationalizing the denominator of 1/(√7 - 2), we get (√7 + 2)/3.