What is the perfect square of root 500?

1 Answer
Jun 22, 2018

Answer:

#=10sqrt(5)#

Explanation:

There is not a "perfect square" of #sqrt(500)#, here is why:

#=sqrt(500)# has the prime factors:

#=sqrt(5*5*5*2*2)#

#=sqrt(5^2*5*2^2)#

#=5*2*sqrt(5)#

#=10*sqrt(5)#

Since 5 is not a perfect square it cannot be removed from the radical in an exact form, i.e. #sqrt5# is an irrational number.