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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Ch.8 Roots and Radicals - Intermediate Algebra @ OpenStax
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Estimating Higher Roots Between Consecutive Whole Numbers
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As an inventory specialist, you need to determine the side length of a perfectly cubic storage bin that holds 300 cubic feet of material. The exact side length is feet. Using the method of estimating higher roots by finding consecutive perfect powers, between which two whole numbers does the side length of this bin lie?
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