# How do you simplify #3/sqrt(7)#?

##### 1 Answer

Aug 9, 2016

#### Explanation:

Simplifying this fraction means expressing it without the radical on the denominator. This is called

#color(blue)"rationalising the denominator"#

To do this we make use of the following fact.

#color(red)(|bar(ul(color(white)(a/a)color(black)(sqrtaxxsqrta=(sqrta)^2=a)color(white)(a/a)|)))#

#rArrsqrt7xxsqrt7=7# Since this is a fraction, if we multiply the denominator by some value then we must multiply the numerator by the same value.

multiply both numerator and denominator by

#sqrt7#

#rArr3/sqrt7xxsqrt7/sqrt7=(3xxsqrt7)/(sqrt7xxsqrt7)=(3sqrt7)/7#