What is the exact value of the square root of 32 over 5 the square root of 14?

1 Answer
Oct 6, 2015

Answer:

#(4sqrt7)/35#

Explanation:

#sqrt32/(5sqrt14)#

Simplify #sqrt32#.

#sqrt(2xx2xx2xx2xx2)/(5sqrt14)=#

#sqrt(2^2xx2^2xx2)/(5sqrt14)=#

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

#(2xx2sqrt(2))/(5sqrt14)=#

#(4sqrt2)/(5sqrt14)#

Rationalize the denominator.

#(4sqrt2)/(5sqrt14)xx(sqrt14)/sqrt14=#

#(4sqrt2sqrt14)/(5xx14)=#

#(4sqrt28)/70=#

Simplify #(4sqrt28)#.

#(4sqrt(2xx2xx7))/70=#

#(4sqrt(2^2xx7))/70=#

#(4xx2sqrt7)/70=#

#(8sqrt7)/70#

Simplify.

#(4sqrt7)/35#