How do you simplify sqrt(24x^3yz)?

1 Answer
Sep 23, 2015

=2x sqrt(6 x y z)

Explanation:

Fully factorising all terms (to assist clarity)

sqrt(24 x^3 y z) = sqrt(2 * 2 * 2 * 3 * x * x * x * y *z)

Collecting terms that can be expressed as squares

= sqrt( 2^2 * 2 * 3 * x^2 * x * y * z)

Taking squared terms outside the square root sign (taking their square roots whilst doing so)

= 2 x sqrt(2 * 3 * x * y * z)

Reforming the compound number from the residua for neatness

= 2x sqrt(6 x y z)