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For which of the following positive integers is the square o [#permalink]
Translating the words to mathematical representation we get

\(\frac{x^2}{\sqrt[3]{x}} = 9x\)

\(x^2 = 9x \sqrt[3]{x}\)

\(x^2 = 9x \times x^{\frac{1}{3}}\)

\(x^2 = 9 \times x^{\frac{4}{3}}\)

\(x^2 = 9({x^\frac{2}{3}}^2)\)

\(x^2 = 3^2 \times ({x^\frac{2}{3}}^2)\)

Taking the square root on both sides, we get

\(x = 3 \times x^{\frac{2}{3}}\)

rearranging the terms

\(x \times x^{\frac{-2}{3}} = 3\)

\(x^{\frac{1}{3}} = 3\)

cubing both sides to get the value of \(x\) on the LHS

\(x = 3^3\)


The answer is D
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