How do you simplify #sqrt(20a^13 b) * sqrt(8a^14 b^12)#?

1 Answer
Tony B
Apr 23, 2016

#4a^13b^6sqrt(10ab)#

Explanation:

Look for values that can be squared. These can be taken outside the square root.

As an example, note that #(a^2)^7=a^(2xx7)=a^14#

Given:#" "sqrt(20a^13b)" "xx" "sqrt(8a^14b^12)#

Write as:#" "sqrt(2^2xx5xx(a^2)^6xxaxxb)xxsqrt(2^2xx2xx(a^2)^7xx(b^2)^6)#

#=>2a^6sqrt(5ab) xx2a^7b^6sqrt(2)#

#=>4a^13b^6sqrt(10ab)#

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