simplify square root?

Question

sqrt 32m^3n^4p^6

Answer 1

sqrt(x) is another way of showing x^(1/2)


When you take x^2 and raise it to the third power, you get x^6 by multiplying the powers (2 and 3 in this case)
So when you take the sqrt of x^2 [shown by sqrt(x^2), or ((x^2)^(1/2))], you multiply the two powers and get 2/2, or 1, making the answer x in this case.

Also, when you multiply x^2 by x^3 you get x^5 by adding the powers (2 and 3 in this case). This means that you can also take x^5 and break it up into (x^4)*(x) so that it will be easier to raise each part to the 1/2. The result:
sqrt(x^5)
sqrt((x^4)*x)
sqrt(x^4)*sqrt(x)
(x^2)*sqrt(x)

Can you solve it now?

Answer 2

Take all the perfect squares out of the radical.

32 contains the perfect square 16 = 4^2, so 16 comes out.
m^3 contains the perfect square m^2, so that comes out.
n^4 = (n^2)^2 and p^6 = (p^3)^2 are already perfect squares, so they can both come out. You end up with

4 m n^2 p^3 sqrt(2 m)

Answer 3

=sqrt(2^5*m^3*n^4*p^6)
=2^2*m*n^2*p^3*sqrt(2m)
=4m n2 p3 sqrt(2m)

Answer 4

Here is a web site

And it has examples of how to find the squar root.

Answer 5

Divide both sides by 0 :: 0 = infinity; simple