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

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Answer 1 · 2015-09-23T16:24:43

#=2x sqrt(6 x y z)#

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)#