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The cube root of $125216$ is ____.

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Detailed Solution

The cube root of

125216

56 .

The given number is

125216 .

Find prime factors of

125216 .

1252163 = 5 × 5 × 5 2 × 2 × 2 × 3 × 3 × 3 3

Make three groups of factors.

5 × 5 × 5 2 × 2 × 2 × 3 × 3 × 3 3 = 5 2 × 3 5 2 × 3 5 2 × 3 3 = 5 2 × 3 3 3

Simplify to get the cube root.

1252163 = 5 2 × 3 3 3 = 5633 = 56

∴ 1252163 = 56

Thus, the cube root of

125216

56 .

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