# What is the square root of 4.5?

##### 1 Answer

Sep 15, 2015

#### Explanation:

You know that

#4.5 = 45/10#

This means that you can write

#sqrt(4.5) = sqrt(45/10) = sqrt(45)/sqrt(10)#

Since

#sqrt(45)/sqrt(10) = sqrt(3 * 3 * 5)/sqrt(10) = (3sqrt(5))/sqrt(10)#

Rationalize the denominator by multiplying the faction by

#(3sqrt(5))/sqrt(10) * sqrt(10)/sqrt(10) = (3 * sqrt(50))/10#

This can be further simplified to

#3/10 * sqrt(50) = 3/10 * sqrt(5^2 * 2) = 3/10 * 5 * sqrt(2) = color(green)(3/2 * sqrt(2))#