Video: Estimating a Cube Root

Identify which of the arrows represents the position of ∛23.

01:39

Video Transcript

Identify which of the arrows represents the position of the cube root of 23.

In order to answer this question, let’s firstly consider the cube numbers. In order to cube a number, we multiply the number by itself and then itself again. Therefore, one cubed is equal to one, two cubed is equal to eight, three cubed is equal to 27. This list would continue for four cubed, five cubed, and six cubed, as shown. We know that cube rooting is the inverse or opposite of cubing. Therefore, the cube root of eight is two, the cube root of 27 is three, the cube root of 64 is four, and so on.

We’ve been asked to identify the arrow that represents the cube root of 23. 23 lies between the two cubed numbers eight and 27. This means that the cube root of 23 is greater than the cube root of eight but less than the cube root of 27. These values are equal to two and three, respectively. The cube root of 23 lies between the integer values two and three. This means that the correct arrow is arrow b. The radical, the cube root of 23, lies between two and three.

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