### Video instructions and help with filling out and completing Which Form 5495 Index

Instructions and Help about Which Form 5495 Index

In this video we're going to look at simplifying certs but before we start simplifying them let's just remind ourselves what they are thirds are basically nasty square roots if you have the square root of 10 I'll call that a nasty square root because if you do it on a calculator square root of 10 and some calculators you have to press the SD button it's a nasty decimal therefore that is a third whereas if I did the square root of 16 well the square root of 16 is 4 because 4 times 4 is 16 so that's not 1/3 because root of 16 is just 4 and 4 is an integer a whole number so this one is a surd over here this one here is not the basic thing is thirds on nursery square root square roots which come out to be nasty decimals so we're going to look at simplifying some SERDES the first one we're going to look at is simplifying root 40 and you might say well what what we're trying to do in simplifying so it's what you're trying to do is get the smallest number possible inside the square root sign and the other numbers outside the square root sign that's fine and the way to do it is to try and spot what two numbers multiply together to give you 40 okay so one times forty two times 25 times eight four times ten there are various different numbers and multiplied together to give you 40 and you're looking for a pair of numbers where one of them is a square number and if I go for four times by ten four is a square number and that's the one I'm going to use you're always looking for a pair of numbers you'd multiply together to give you the number inside the square root sign when one of them is a square number so the square root of 40 is a square root of that sum and I write that like that that's some inside the square root sign and then what you can do is this if you have the square root of two numbers which are multiplied together and also works if they're divided it does not work if you're adding or taking away but if you're multiplying together you can say it's a square root of the first number times by the square root of the second number now I'll emphasize again you can only do this if it's a time sign or a device sign you cannot do that if it's adding or taking but hang on a minute the square root of 4 that's just 2 because 2 times 2 is 4 square root of 10 we'll leave that there now because there's no square number that goes into 10 I cannot simplify that side because square numbers are 1 well that doesn't actually help us 4 doesn't go into 10 9 doesn't go into 10 the next square number is bigger than 10 so that doesn't help us so root 4 C can be simplified to 2 root 10 and what it looks more complicated in mathematical terms has been simplified because the number inside the square root is smaller so we're going to look at some more number 2 we'll have a look at root 50 so the first thing to do is to think what numbers multiply together to give me 50 and can I come up with any pair of numbers that multiply together or one of them the square number well hopefully you want to come up with 25 times by 225 times by 2 is the same as 50 so that means root 50 is the same as the square root of a sum 25 times by 2 and because there's a multiplying sign in here we can say that's same as root 2 25 times by square root of 2 the square root of 25 is 5 I'll leave the root 2 there so root 50 it's the same as 5 root 2 I've simplified that third because the number in the square root sign is smaller than it was at the beginning of the question as well as doing this to individual SERDES sometimes you can have questions which evolve more than one the third one we're going to look at now is to simplify root 48 plus root 27 so you may have a sum here involving square roots involving SERDES 48 where you can get 48 from six times by 8 from 2 by 24 we're really looking for one which has got a square number in it so it's useful just think square numbers of times table C 9 times table 9 18 27 36 45 54 that hasn't helped next square number 16 so we could 16 32 48 64 48 so 16 times by 3 is 48 so I can rewrite my 48 like that about 27 27 is 9 times by 3 so root of 27 I can write like that and these two sums are being added together root 16 times root 3 using the same trick is videoed up here splitting them up that's the same as root 16 times by root 3 and over here root 9 times 3 is the same as the square root of 9 times the square root of 3 I'm adding those bits together the square root of 16 is just 4 so this left-hand side is the same as for lots of root 3 on the right of my plus root 9 is 3 so I've got 3 lots of root 3 so I've got 4 lots of root 3 plus 3 lots of root 3 it probably won't surprise you to realize that's 7 lots of root 3 you think of for some things plus 3 and the same thing it's 7 of those things so 4 root 3 plus