Question

Rationalize the denominators of the following:

1/(√7 - √6)

Answer 1

1/(√7 - √6)

We need to multiply the numerator and denominator of 1/(√7 - √6) by, √7 - √6, to get

1/(√7 - √6) x (√7 + √6) / (√7 + √6)

= (√7 + √6) / (√7 - √6)(√7 + √6).

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

1/(√7 - √6) = (√7 + √6) / ((√7)2 - (√6)2

= (√7 + √6) / 7 - 6 = √7 + √6

Therefore, we conclude that on rationalizing the denominator of 1/(√7 - √6),we get √7 + √6.