 So we've already discovered what SIRDS are in this video and how to calculate with them in these videos. We're now going to look at the final piece of the SIRDS puzzle at what rationalising the denominator is. We know that the denominator is the bottom part of a fraction. So have a look at these. What do you notice about those that are rationalised and those that aren't? Rationalising the denominator is when we move a square root from the bottom, the denominator, to the top, the numerator. For a SIRDS to be in its simplest form, the denominator cannot be irrational. It can't have a square root in its denominator. It's not wrong, it's just not considered the simplest form. Let's have a look at how we move the root. Multiply both the top and bottom by the root. And we get 1 multiplied by root 2 which equals root 2 and root 2 multiplied by root 2 which is 2 because the rules of SIRDS means that we do 2 times 2 which is 4 and the square root of 4 is 2. You can check this yourself on your calculator. Type in 1 over root 2, press equals and the calculator will rationalise it for you. But this won't get you marks in your exams. You've got to show the working but do use it just to check yourself. So here's one for you to do. Rationalise this fraction. Don't worry about the 3, leave it where it is in the denominator. Pause the video, give the question a go and click play when you're ready. Did you get it right? 5 root 7 over 21. So let's have a look at a trickier example. I'll do the first bit for you to get you started. We need to multiply by the whole of the denominator but change the sign. So think of expanding brackets and the difference of two squares. We would get a squared plus a b minus a b minus b squared and the plus a b and minus a b would cancel each other out leaving us with just a squared minus b squared. This is exactly what we want to do here. We want to cancel out the SIRDS. So expand the denominator brackets and what you get. Pause the video, work out and click play when you're ready. You should have got 11. So going back to the question we can simplify by expanding brackets and we get this 12 plus 3 root 5 over 11. So give this question a go yourself. Pause the video, work out the answer and click play when you're ready. Did you get it right? So there you have rationalizing the denominator which is just a fancy way of saying remove any square roots from the denominator. We have to do this to ensure that we fully simplified our SIRDS.