If [3]12167* 16384 = x*11.5, then what is the value of x?

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PS · Problem Solving

705-805

Roots

If $\sqrt[3]{12167}\sqrt{16384} = x11.5$ , then what is the value of x?

Answer Choices

Correct answer marked below

A

204

B

234

256

Correct

D

272

E

286

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Explanation

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Official Explanation

Official

\sqrt[3]{12167}*\sqrt{16384} = x*11.5

Taking cube and square root of respective numbers:

23 * 128 = x * 11.5

…

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What this question tests

What it tests

Your handling of square and higher roots, including simplifying radicals.

Common trap

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.

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If 121673∗16384=x∗11.5\sqrt[3]{12167}*\sqrt{16384} = x*11.5312167​∗16384​=x∗11.5, then what is the value of x?