Problem 5 · 2012 Math Kangaroo
Easy
Algebra & Patterns
number-systems
The number \(\sqrt[3]{2\sqrt{2}}\) is equal to
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Answer: B — \(\sqrt{2}\)
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Hint 1 of 2
Turn every root into a power of 2 so the exponents do the work.
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Hint 2 of 2
Once the inside is a single power of 2, the cube root just divides that exponent by 3.
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Approach: rewrite everything as a power of 2
- Inside the root, \(2\sqrt{2} = 2\cdot 2^{1/2} = 2^{3/2}\).
- The cube root divides the exponent by 3: \(\left(2^{3/2}\right)^{1/3} = 2^{1/2}\).
- So the value is \(\sqrt{2}\), choice B.
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