 Lucy and in this video we're going to look at SIRDS. But what on earth are SIRDS? A SIRD is a square root which cannot be reduced to a whole number. What does that even mean? Let's have a look at an example. So square root 25 and square root 9 sixteenths are not SIRDS because even though they are inside a square root sign, they can be evaluated. We can simplify them. Whereas for example square root 2 and square root 3 cannot be simplified. They are irrational. If you type them into a calculator you get lots of decimal places that carry on forever and the numbers cannot be written as fractions. So have a look at this table. See which are SIRDS and which aren't. SIRDS are actually really useful. See how much easier it is to write square root 2 rather than all of those decimals and actually in Pythagoras we come across them a lot because it is much more accurate to leave it as a SIRD than to round the decimal places. So square root 1044 or the simplified SIRD form of 6 root 29 is much more accurate and easier than writing 31.31 etc. So not all square roots are SIRDS but all SIRDS are square roots. Let's have a look at simplifying SIRDS. 6 root 29 is the simplified version of square root 1044 but we'll start with much simpler examples. Have a look at these simplified SIRDS. How have they been simplified? Can you spot what is happening in the working column? How the working connects to the original SIRD? Pause the video, have a think and click play when you're ready. Did you notice how when doing the working we look for a square number that goes into each SIRD and then what it multiplies by? So root 4 is the square number multiplied by 2 makes 8. Again root 4 is the square number multiplied by 3 makes 12. In this one root 9 is the square number multiplied by 3 makes 27. It could be any square number 16 25 36 49 make sure you know your square numbers. Just a quick thing though root 180 I wouldn't necessarily know that 36 goes into it but I do know that 9 does so I could start by simplifying it to root 9 multiplied by root 20 and root 20 isn't fully simplified so we just keep going 3 root 4 root 5 and all the way down to 6 root 5. So give these questions a go pause the video work out the answers and click play when you're ready to check. Did you get them right? If not just make sure that you simplified them fully until no more square numbers factor into them. So that is the beginning of SIRDS we now know what they are and how to simplify them. In the next video we're going to look at how to multiply and divide with SIRDS and then also how to add and subtract with them.