1Cademy - Approximating Higher Roots with a Calculator

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Approximating Square Roots with a Calculator

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Approximating Higher Roots with a Calculator

Just as a calculator's $\sqrt{x}$ key provides decimal approximations for square roots, the $\sqrt[y]{x}$ key (or its equivalent for higher indices) is used to find decimal approximations for roots with an index greater than $2$ . For a number that is not a perfect $n$ th power, the calculator returns a rounded decimal approximation rather than an exact value. For example, using a calculator to evaluate $\sqrt[4]{93}$ yields an approximation such as $3.105422799$ , which can be rounded to two decimal places as $3.11$ . To verify that this is an approximation, raising the rounded result to the fourth power gives $(3.11)^4 \approx 93.54951841$ , which is close to $93$ but not exactly $93$ . The approximation symbol $\approx$ indicates that the value is rounded.