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

1 Answer
Sep 23, 2015

Answer:

#=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)#