Example

Rounding 493\sqrt[3]{49} and 514\sqrt[4]{51} to Two Decimal Places

To evaluate higher roots that are not perfect powers, we use a calculator and then round the result.

For example, to approximate 493\sqrt[3]{49}: Step 1: Use the calculator's xy\sqrt[y]{x} key to find the cube root. The display shows 3.6593057103.659305710\dots Step 2: Round to two decimal places. The hundredths digit is 55 and the next digit is 99. Since 959 \geq 5, we round up to get 3.663.66. Thus, 4933.66\sqrt[3]{49} \approx 3.66.

Similarly, to approximate 514\sqrt[4]{51}: Step 1: Use the calculator to find the fourth root. The display shows 2.67234511772.6723451177\dots Step 2: Round to two decimal places. The hundredths digit is 77 and the next digit is 22. Since 2<52 < 5, the digit stays the same, giving 2.672.67. Thus, 5142.67\sqrt[4]{51} \approx 2.67.

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Updated 2026-05-01

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