How do you simplify sqrt(63c^3d^4f^5)63c3d4f5?

2 Answers
Mar 21, 2017

3cd^2f^2*sqrt(7cf)3cd2f27cf

Explanation:

sqrt(63c^3d^4f^5)63c3d4f5

:.=(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)

Mar 21, 2017

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)