How do you simplify (4 sqrt 45) / (5 sqrt 8)?

2 Answers
Serena D.
May 3, 2018

(3sqrt10)/5

Explanation:

Remember that perfect squares can be taken out of radicals

(4sqrt45)/(5sqrt8)

(4sqrt(9*5))/(5sqrt(4*2))

(4*3sqrt5)/(5*2sqrt2

(12sqrt5)/(10sqrt2)

(6sqrt5)/(5sqrt2) rarr Don't forget to rationalize the denominator

(6sqrt(5*2))/(5sqrt(2*2))

(6sqrt10)/(5sqrt4)

(6sqrt10)/10

(3sqrt10)/5

Shantelle
May 3, 2018

14 2/5 or 14.4

Explanation:

(4sqrt45)/(5sqrt8)

First, find the largest factors of 45 and 8 that can be square rooted.
9 * 5 = 45, and sqrt9 = 3
4 * 2 = 8, and sqrt4 = 2

Now we put it back into the expression like this:
(4sqrt(9 * 5))/(5sqrt(4 * 2)

Split up the square root:
(4sqrt9sqrt5)/(5sqrt4sqrt2)

Take square root of 9 and 4:
(4*3sqrt5)/(5*2sqrt2)

Multiply:
(12sqrt5)/(5sqrt2)

Square numerator and denominator:
(12sqrt5)^2/(5sqrt2)^2

(144 * 5)/(25 * 2)

720/50

Divide:
14 2/5 or 14.4

Hope this helps!

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
5388 views around the world
You can reuse this answer
Creative Commons License