How do you simplify #(7sqrt100)/sqrt500#?

1 Answer
Oct 1, 2015

Answer:

The answer is #(7sqrt5)/5#.

Explanation:

#(7sqrt100)/(sqrt500)#

Numerator
Write the prime factorization for #100# and simplify. Use the square root rule #sqrt(a^2)=absa# .

#7sqrt100=7sqrt(10xx10)=7sqrt(10^2)=7xx10=70=#

#70/(sqrt500)#

Denominator
Write the prime factorization for #sqrt500# and simplify. Again use the square root rule #sqrt(a^2)=absa# .

#sqrt500=sqrt(2xx2xx5xx5xx5)=sqrt(2^2xx5^2xx5)=2xx5sqrt5=10sqrt5#

Recombine the numerator and denominator.

#70/(10sqrt5)#

Rationalize the denominator.

#(7)/(sqrt(5)) * (sqrt5)/(sqrt5)=#

#(7sqrt5)/(sqrt(25))#

Write the prime factors for #25#.

#sqrt25=sqrt(5xx5)=#

#sqrt25=sqrt(5^2)#

Apply the square root rule #sqrt(a^2)=absa# and simplify.

#(7sqrt5)/5#