Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 2 • Question 2

Circle the cube number. [A] 16 [B] 8 [C] 9 [D] 75.

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Video Transcript

Circle the cube number. The options are 16, eight, nine, or 75.

First, we need to remind ourselves what is meant by a cube number. A cube number is the result of taking an integer, multiplying it by itself, and then multiplying it by itself again. For example, one is a cube number because it’s what we get when we take the number one, multiply it by itself, and then multiply it by itself again. One multiplied by one multiplied by one is also written as one cubed, hence the name cube number.

The next cube number two cubed is found by taking two, multiplying by two, and then multiplying by two again. Two multiplied by two is four and multiplying by two gives eight. We see that eight is one of the options we were given. So we can circle it because eight is a cube number. Let’s just check that none of the other options we’ve been given are cube numbers.

The next cube number is found by evaluating three multiplied by three multiplied by three. Three multiplied by three is nine and multiplying by three again gives 27. So the next cube number is 27. We can, therefore, eliminate 16 and nine because we’ve already gone past each of these numbers in our search for the cube numbers.

In fact, nine and 16 are both a different type of number; they’re both square numbers. Nine is equal to three squared, three times three, and 16 is equal to four squared, four times four.

Let’s keep going in our search for the cube number though so we can check whether or not 75 is a cube number. Next, we have four multiplied by four multiplied by four which is 64 and then five multiplied by five multiplied by five which is 125. At this point, we can eliminate 75 because our list of cube numbers already exceeds 75.

Of the four options then the only one which is a cube number is eight, which is equal to two cubed.

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