# How do you simplify #sqrt3/-sqrt21#?

##### 1 Answer

Oct 12, 2015

#### Answer:

#### Explanation:

The firs thing to notice here is that you can write

#21 = 7 * 3#

This means that the denominator of the fraction will be equivalent to

#sqrt(21) = sqrt(3 * 7) = sqrt(3) * sqrt(7)#

SInce

#sqrt(3)/(-sqrt(21)) = -color(red)(cancel(color(black)(sqrt(3))))/(color(red)(cancel(color(black)(sqrt(3)))) * sqrt(7)) = - 1/sqrt(7)#

Next, *rationalize the denominator* by multiplying the fraction by

#-1/sqrt(7) * sqrt(7)/sqrt(7) = -sqrt(7)/(sqrt(7) * sqrt(7)) = -sqrt(7)/sqrt(7 * 7) = color(green)(-sqrt(7)/7)#