### 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.