Question

How do you simplify `sqrt(63c^3d^4f^5)`?

Answer 1

`3cd^2f^2*sqrt(7cf)`

Explanation:

`sqrt(63c^3d^4f^5)`

`:.=(63c^3d^4f^5)^(1/2)`

`:.=(7*3*3*c^3d^4f^5)^(1/2)`

`:.=(7*3^2c^3d^4f^5)^(1/2)`

`:.=(7^(1/2)*3^(2 xx 1/2)c^(3 xx 1/2)d^(4 xx 1/2)f^(5 xx 1/2))`

`:.=(7^(1/2)*3^1*c^(3/2)*d^(4/2)*f^(5/2))`

`:.=sqrt7*3*sqrt(c^3)*sqrt(d^4)*sqrt(f^5)`

`:.=3d^2*sqrt(7c^3f^5`

`:.=3d^2sqrt(7*c*c*c*f*f*f*f*f)`

`sqrta*sqrta=a`

`:.=3cd^2f^2sqrt(7cf)`

Answer 2

`3cd^2f^2sqrt(7cf)`

Explanation:

Given`:" "sqrt(63c^3d^4f^5)`

As soon as you see a square root you know that you are looking for squared values within that root. You can 'take outside' the root all those squared values.

Write as:`" "sqrt( 3^2xx7xxc^2xxcxx(d^2)^2xx(f^2)^2xxf)`

Taking the squared values 'outside' the root giving:

`3cd^2f^2sqrt(7cf)`