# How do you rationalize the denominator and simplify #(5sqrt6)/sqrt10#?

##### 3 Answers

#### Explanation:

multiply by

#### Explanation:

In order to rationalize the denominator, you can multiply by

With

Next, you can simplify

Lastly, just cancel out the 2 in the numerator and denominator, and you get the answer of

#### Explanation:

#"using the "color(blue)"laws of radicals"#

#•color(white)(x)sqrtaxxsqrtbhArrsqrtab#

#•color(white)(x)sqrtaxxsqrta=a#

#"To rationalise the denominator that is eliminate the "#

#"radical from the denominator"#

#"multiply numerator/denominator by "sqrt10#

#rArr(5sqrt6)/sqrt10#

#=(5xxsqrt6xxsqrt10)/(sqrt10xxsqrt10)#

#=(5xxsqrt60)/10#

#=(5xxsqrt(4xx15))/10#

#=(5xxsqrt4xxsqrt15)/10#

#=(5xx2xxsqrt15)/10=(cancel(10)sqrt15)/cancel(10)=sqrt15#