Question

What is the simplest form of the expression?
sqrt 625x^20y^8

Answer 1

`\sqrt {625x^(20)y^8} = 25x^(10)y^4`

Answer 2

We have to simplify the expression , it means

we have to try to factor every number and and every variable , and try to factor out those which can be factored out from the square root

first number is 625

Lets try to write prime factors of 625

625 = 5*5*5*5

Next are x^20 and y^8

Now square root will divide each exponent by 2

So we get

`√(625x^20y^8)`

=
`\sqrt{5*5*5*5*x^(20)y^8}`

=
`\sqrt{5^4x^(20)y^8}`

=
`5^2 x^(10) y^4`

=
`=25x^(10) y^4`

So this is the answer.