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)

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
1756 views around the world
You can reuse this answer
Creative Commons License