Question

find the cube root of the 389017
through Estimate


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Answer 1

$Answer$ : -

Okay, divide the number in groups of three digits right to left: 389 and 017. There are two groups, so the answer (or its integer part) is two digits.

First group is 343 ≤ 389 ≤ 512, so the first digit in the answer is 7.

Conjecture: it is a perfect cube. If it is a perfect cube the rightmost digit in the answer shall be 3 (so its cube ends 7) So let's check if 73 is the answer.

73 × 73 = 4900 + 420 + 9 = 5,329.

5,329 × 70 = 15,000 + 900 + 60 + 27 = 15,397.

And those two numbers do add up to 389017 .

So that is the answer.

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