How do you simplify #sqrt72-sqrt50#?

1 Answer
Nov 6, 2015

Answer:

#sqrt 72-sqrt 50=sqrt 2#

Explanation:

#sqrt 72-sqrt 50#

Write the prime factors for #72#.

#sqrt(2xx2xx2xx3xx3)-sqrt 50#

Group like terms in pairs.

#sqrt((2xx2)xx2xx(3xx3))-sqrt 50#

Simplify.

#sqrt(2^2xx2xx3^2)-sqrt 50#

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

#2xx3sqrt2-sqrt50#

#6sqrt 2-sqrt 50#

Write the prime factors for #50#.

#6sqrt 2-sqrt(2xx5xx5)#

Group like terms in pairs.

#6sqrt 2-sqrt(2xx(5xx5))#

Simplify.

#6sqrt 2-sqrt(2xx5^2)#

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

#6sqrt 2-5sqrt2=#

#sqrt 2#