Question - Finding Closest Integer to Cube Root
Solution:
The expression in the question is the cube root of √2, which can be rewritten using exponents as (2^(1/2))^(1/3). When we multiply the exponents, we get 2^(1/6). To find out which integer this is closest to, we can look for small integers and their sixth powers to compare.The sixth power of 1 is 1 (since 1^6 = 1), and the sixth power of 2 is 64 (since 2^6 = 64). The number 2^(1/6) will be somewhere between 1 and 2, but closer to 1 since 2 is much larger when raised to the sixth power.Therefore, the integer closest to the cube root of √2 is 1.
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