GMATPrepNow wrote:
If \((\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})\), then \(x=\)
A) \(\frac{1}{8}\)
B) \(\frac{1}{2}\)
C) \(\sqrt[3]{\frac{1}{2}}\)
D) \(\sqrt[3]{2}\)
e) \(2\)
Useful root property: \(\frac{\sqrt[n]{x}}{\sqrt[n]{y}}=\sqrt[n]{\frac{x}{y}}\)Given: \((\sqrt[3]{4})(\sqrt{5.5})=(\sqrt{22})(\sqrt[3]{x})\)
Divide both sides by \(\sqrt{5.5}\) to get: \(\sqrt[3]{4}=\frac{(\sqrt{22})(\sqrt[3]{x})}{\sqrt{5.5}}\)
Divide both sides by \(\sqrt[3]{x}\) to get: \(\frac{\sqrt[3]{4}}{\sqrt[3]{x}}=\frac{\sqrt{22}}{\sqrt{5.5}}\)
Apply above
property to both sides to get: \(\sqrt[3]{\frac{4}{x}}=\sqrt{\frac{22}{5.5}}\)
Simplify right side: \(\sqrt[3]{\frac{4}{x}}=\sqrt{4}\)
Simplify right side: \(\sqrt[3]{\frac{4}{x}}=2\)
Raise both sides to the power of 3 to get: \((\sqrt[3]{\frac{4}{x}})^3=2^3\)
Simplify: \(\frac{4}{x} = 8\)
Solve: \(x = \frac{4}{8} = \frac{1}{2}\)
Answer: B
Cheers,
Brent
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