How do you simplify #sqrt(28a^3b^2)#?

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Answer 1 · 2016-05-27T14:44:30

#= 2ab sqrt(7a#

#sqrt(28a^3b^2#

Prime factorising #28# (expressing a number as a product of its prime factors):

#28 = color(green)( 2 * 2 * 7#

#= sqrt( color(green)(2 * 2 * 7) * a^3b^2#

#= sqrt( color(green)(2 ^2 * 7) * color(blue)(a^2) * a * color(blue)( b^2#

#= 2 * color(blue)(a * b) sqrt( color(green)( 7) * a#

#= 2ab sqrt(7a#