Video: Finding the Cube Root of Rational Numbers

Calculate ∛(8/729).

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Video Transcript

Calculate the cube root of eight divided by 729.

The cube root of any fraction, 𝑎 divided by 𝑏, can be calculated by splitting the numerator and the denominator and cube-rooting each of them individually. In this case, we need to calculate the cube root of eight and separately the cube root of 729. We know that two cubed is equal to eight, as two multiplied by two multiplied by two is equal to eight. Therefore, the cube root of eight is equal to two. This means that our numerator is two.

Nine cubed is equal to 729, as nine multiplied by nine is 81 and 81 multiplied by nine is 729. This means that the cube root of 729 is equal to nine. Therefore, our denominator is nine.

This means that the answer to the calculation the cube root of eight divided by 729, or eight seven hundred and twenty-ninths, is equal to two-ninths. We could check this by cubing our answer. Two-ninths cubed is the same as two-ninths multiplied by two-ninths multiplied by two-ninths. This is equal to eight seven hundred and twenty-ninths. Therefore, our answer is definitely correct.

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