How do you evaluate #\sqrt{45x^{3}}\cdot \sqrt{3x^{4}}#?

1 Answer
EZ as pi
Dec 16, 2016

#3x^3sqrt(15x)#

Explanation:

When multiplying or dividing square roots, you can combine two or more into one square root.

#sqrt(45x^3) xx sqrt(3x^4) = sqrt(45 xx 3 xx x^3 xx x^4)#

Write as a product of prime factors and even powers if possible:

#= sqrt(3xx3xx3xx5xxx^6 xx x)#

#= sqrt(3^2 xx3xx5xxx^6 xx x)#

Find square toots where possible:

#=3x^3sqrt(15x)#

Note that there is little point in finding the full answer under the root, as #sqrt(135x^7)#

because it will have to be broken down again anyway.

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