Estimating Higher Roots Between Consecutive Whole Numbers
The technique used to estimate square roots can be extended to estimate higher-order roots. To estimate an th root like , locate the radicand between two consecutive perfect th powers. Because the th root function preserves order, the th root of the number will lie between the th roots of those perfect powers. For instance, falls between the consecutive perfect cubes and ( and ). Therefore, the cube root of must lie between and : . This bounding method provides a quick numerical estimate for any root index without using a calculator.
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Intermediate Algebra @ OpenStax
Ch.8 Roots and Radicals - Intermediate Algebra @ OpenStax
Algebra
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Estimating Higher Roots Between Consecutive Whole Numbers