Video: AQA GCSE Mathematics Higher Tier Pack 2 • Paper 1 • Question 6

Barbara works out the answer to −4 (8.5 − √50.4). She says the answer is positive. Is she correct? You must show your working.

02:05

Video Transcript

Barbara works out the answer to negative four multiplied by 8.5 minus the square root of 50.4. She says the answer is positive. Is she correct? You must show your working.

Let’s look at our sum again. Negative four is being multiplied by whatever the value inside our bracket is. If we recall our rules for multiplying with negative numbers, we know that a negative multiplied by a positive gives us a negative. And we also know that a negative multiplied by a negative gives us a positive answer.

So really we need to establish whether the value inside the bracket is negative or positive. If it’s negative, we’re multiplying it by another negative answer, and the overall value will be positive. If it’s positive, we’re multiplying it by negative four, so the overall answer will be negative. But how do we decide whether the expression inside the bracket is positive or negative?

We’re first going to need to estimate the value of the square root of 50.4. To do this, we recall the square numbers we know that are near 50.4. 49 is a square number. It’s the result of squaring seven or multiplying seven by itself. And eight squared is 64, so 64 is another square number near to 50.4.

In reverse, this means that the square root of 49 is seven and the square root of 64 is eight. So the square root of 50.4 must be somewhere between these two numbers. Actually, it will be seven and a little bit. So inside the bracket, we have 8.5 minus seven point something, seven and a bit.

No matter what the value of the bit, 8.5 will be greater than seven and a bit. And therefore, our overall expression inside the bracket is positive. We’re multiplying that by negative four. And a negative multiplied by a positive gives us a negative solution. In fact, Barbara is incorrect. The solution, the answer, to this problem will actually be negative.

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