What is the simplest radical form of #-5sqrt21*(-3sqrt42)#?

1 Answer
Stefan V.
Jul 24, 2015

#315sqrt(2)#

Explanation:

The first thing to notice here is that you're multiplying two negative numbers, #-5sqrt(21)# and #-3sqrt(42)#, so right from the start you know that the result will be positive.

Moreover, using the commutative property of multiplication, you can write

#-5 * sqrt(21) * (-3 * sqrt(42)) = [-5 * (-3)] * sqrt(21) * sqrt(42)#

ANother important thing to notice here is that #21# is actually a factor of #42#

#42 = 21 * 2#

This means that the expression becomes

#15 * sqrt(21) * sqrt(21 * 2) = 15 * underbrace(sqrt(21) * sqrt(21))_(color(blue)("=21")) * sqrt(2)#

which is equivalent to

#15 * color(blue)(21) * sqrt(2) = color(green)(315sqrt(2)#

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