What is the value of Square root of 1^3+2^3+3^3+4^3+5^3+6^3+7^3+8^3+9^3+10^3?

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Answer 1

Evaluate: 1+8+27+64+125+216+343+512+729+1000=3025=55^2. Square root=55.

Note that progressively the sum of each term up to and including the term is a perfect square:

Squares of 1, 3, 6, 10, 15, 21, 28, 36, 45, 55. The gap between each of these increases by 1 as the series progresses. Each term is the sum of the natural numbers: n(n+1)/2. When n=10, for example, this expression is 55. Sum to n terms of n^3=n^2(n+1)^2/4.