Question 182355
{{{5sqrt(32) - 7sqrt(8)}}}
Begin by factoring terms inside the radical (w/prime numbers):
{{{5sqrt(2*2*2*2*2) - 7sqrt(2*2*2)}}}
Then, pull out "pairs" from under the radical:
{{{5(2*2)sqrt(2) - 7(2)sqrt(2)}}}
{{{20sqrt(2) - 14sqrt(2)}}}
Factoring:
{{{sqrt(2)(20 - 14)}}}
{{{sqrt(2)(6)}}}
{{{6sqrt(2)}}}
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{{{2sqrt(15xy^3) * sqrt(30x^3y^2)}}}
Pull out pairs:
{{{(2y)sqrt(15xy) * xy(sqrt(30x))}}}
{{{(2xy^2)sqrt(15xy) * sqrt(30x)}}}
{{{(2xy^2)sqrt(15xy30x)}}}
{{{(2xy^2)sqrt(15xy(2*15)x)}}}
{{{2xy^2(15x)sqrt(2y)}}}
{{{(30x^2y^2)sqrt(2y)}}}