Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 2 • Question 10

Use your calculator to work out ∛286. a) Write down your full calculator display. b) Write down the answer to 2 decimal places.


Video Transcript

Use your calculator to work out the cubed root of 286. Part a) Write down your full calculator display. Part b) Write down the answer to two decimal places.

Part a) is assessing our calculator skills. Do we know how to evaluate a cube root using our calculator? Now the exact button that you use to evaluate a cube root will depend on the model of your calculator. On my calculator, I have a button that looks like this, which is for evaluating a square root. Directly above this button, written in an orange font is the notation for a cube root. So if I want to use this button for a cube root rather than a square root, I have to press shift first. I press shift then this button and then 286 in order to evaluate the cube root of 286.

If you don’t have a button like this on your calculator, you may instead have a button either that says 𝑥 to the power of 𝑦 or 𝑥 and then a little superscript box. This button is for evaluating any power of a number. If we want to use this button, then we need to recall that a cube root actually represents a power of one-third. So the cubed root of 286 is also equal to 286 to the power of one-third.

We can type 286, press either of these buttons, and then type the power in as one-third, either by writing one divided by three or by using the fraction key. And our calculator will then evaluate the cubed root of 286 for us.

In part a), we’re asked to write down our full calculator display. So we need to write down every digit that our calculator gives us on screen in the answer. My calculator gives nine digits after the decimal point. So our answer to part a) is 6.588532275.

In part b), we’re asked to write down the answer to two decimal places. So this time, we’re going to round the cubed root of 286. If we want to round a number to two decimal places, then our deciding digit, which tells us whether we’re rounding up or down, is the number in the next decimal place. That’s the number in the third decimal place, which in this case is an eight.

We can actually ignore all of the following digits because they don’t make a difference to our rounding. As this eight is greater than five, this tells us that we’re going to be rounding up, which means the eight in the second decimal place will round up to a nine. Rounded to two decimal places then, the cubed root of 286 is equal to 6.59.

We can also visualise this on a number line. The two decimal place values either side of 6.588 are 6.58 and 6.59. Exactly halfway between these values is the decimal 6.585. Our value of 6.588, now that we’re ignoring all of the subsequent digits, is between 6.585 and 6.59. It’s in the upper half of this interval, which means it’s closer to 6.59 than it is to 6.58. Therefore, it rounds up to 6.59 to two decimal places.

We can also perform a quick check of our answer by evaluating 6.59 cubed on our calculator, either by typing 6.59 cubed or by typing 6.59 multiplied by 6.59 multiplied by 6.59. This gives 286.191179. It’s not exactly 286 because we rounded our answer. But it’s very close.

So in part a), we found that the cubed root of 286 using our full calculator display is 6.588532275. And in part b), we rounded this value to two decimal places, giving 6.59.

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