What is the square root of 4/125?

1 Answer
Oct 9, 2015

Answer:

#sqrt(4/125)=(2sqrt 5)/(25)#

Explanation:

#sqrt(4/125)#

Simplify.

#(sqrt 4)/(sqrt125)#

Determine the prime factors for #4# and #125#.

#(sqrt(2xx2))/(sqrt(5xx5xx5))#

#(sqrt(2^2))/(sqrt(5^2xx5)#

Apply square root rule #sqrt(a^2)=a#.

#2/(5sqrt 5)#

Rationalize the denominator.

#2/(5sqrt 5)xx(sqrt5)/(sqrt5)=#

#(2sqrt 5)/(5sqrt5sqrt5)=#

Simplify #sqrt 5sqrt 5# to #5#.

#(2sqrt 5)/(5xx5)=#

#(2sqrt 5)/(25)#