Rationalising Denominators

Question

Rationalise the denominator of 21/√7 and simplify the answer.

 

Please explain a) what this question means and b) how to answer it. Thanks :)

Answer 1

In math, we do not want to have a radical (√) in the denominator of a rational expression,  "Rationalizing a denominator" means to multiply the rational expression by a form of one to get the radical out of the denominator.

 

In this case, the "form of one" is just √7/√7:

 

21      √7          21√7          21√7

---- * -----  =  ----------  =  --------  =  3√7

√7     √7         √7*√7            7

 

Voila!  No radical in the denominator,  For that matter, there's no denominator!

Answer 2

to rationalize a denominator means to have a rational number in the denominator's position. (can't have the square root of 7).  So the best way to deal with this is to multiply the numerator and denominator by the square root of 7 and then simplify.