Which is larger:
the tenth root of 10, or the cube root of 2?
Puzzle Copyright © Kevin Stone
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Hint
You don't need to use a calculator.
Answer
Cube root of 2.
Reasoning
We could use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.
But, if you've not got your calculator handy...
We have:
101/10 vs 21/3
Raise each to the power of 30 (since 10 x 3 = 30) to give:
(101/10)30 vs (21/3)30
101/10 x 30 vs 21/3 x 30
103 vs 210
1000 vs 1024
Therefore, the cube root of 2 is larger.
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