Make 𝑟 the subject of this formula. 𝑠 is equal to three 𝑟 squared plus four.
When we change the subject, we rearrange the formula by applying a series of inverse
operations. Remember inverse just means opposite. And if we want to make 𝑟 the subject, we want 𝑟 to be equal to some expression. Let’s consider what’s currently happening to this 𝑟.
The very first thing that has happened to this 𝑟 is it’s been squared. And we know that it’s being squared before being multiplied because in BIDMAS or
BODMAS, indices come before multiplication. After being squared, it’s then multiplied by three. And then, it’s had four added to it.
To apply the inverse of these operations, we’re going to start from the very final
operation. The final operation was adding four. The opposite of adding four is subtracting four. So we’re going to subtract four from both sides of this equation. Doing so and we get 𝑠 minus four is equal to three 𝑟 squared.
The next inverse operation is the opposite to multiplying by three. The opposite of multiplying by three is dividing by three. So we’re going to divide both sides of this equation by three. The simplest way to write divided by three is to write it as a fraction. So we currently have 𝑠 minus four all over three is equal to 𝑟 squared.
The very final inverse operation is the opposite to squaring. The opposite to squaring is square rooting. So we’re going to square root both sides of our equation. And we get 𝑟 is equal to the square root of 𝑠 minus four all over three. That’s not quite it though. Whenever we find a square root, we actually get two solutions: one is a positive and
one is a negative.
So the square root of four, for example, is positive two and negative two. And this is because positive two multiplied by positive two is four. But also a negative multiplied by a negative is a positive. So negative two multiplied by negative two is also four. And that’s where this plus minus comes from.
Now, you wouldn’t lose marks if you’d forgotten to put the plus minus here. But it’s worth being aware of. It’s also really important in this final stage to be clear that we’re finding the
square root of the entire expression 𝑠 minus four over three.
If the examiners have any doubt that we aren’t applying the square root to the whole
of the expression, we could lose that final mark. To be safe, make sure it’s really clear that the square root symbol goes over the
This leaves us with 𝑟 is equal to the square root of 𝑠 minus four over three or 𝑟
is equal to plus or minus the square root of 𝑠 minus four over three.