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

2 Answers
May 3, 2018

Answer:

#(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#

May 3, 2018

Answer:

#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!