SOLUTION: Express the following expression in simplest radical form. All variables represent positive real numbers. SQRT of 27(a^2)b / SQRT of 7(a^3)(b^3)

Question 38208: Express the following expression in simplest radical form. All variables represent positive real numbers.
SQRT of 27(a^2)b / SQRT of 7(a^3)(b^3)
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
From
sqrt27(a^2)b / sqrt7(a^3)(b^3)
we can make it all one root and then cancel as possible, thus we get
sqrt[27(a^2)b / 7(a^3)(b^3)] =
sqrt[27 / 7ab^2]
From here, we need to rationalize the denominator by multiplying top and bottom by sqrt(7a)/sqrt(7a)...so we have
sqrt[27 / 7ab^2] * sqrt(7a)/sqrt(7a) =
sqrt[189a / 49(a^2)(b^2)]
Now 49(a^2)(b^2) is a perfect square so we can remove it from the root...our final answer is
sqrt(189a) / 7ab
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