simplifying subs so i've got square root of 15 i want to simplify it so i'm looking for two numbers at times together to make 50. one of them has to be a square number so i've got the option of 1 4 9 16 25 36 and so on to find the square number you just take a number and times it by itself the answer is a square number so 25 goes into 50 so i can write that first times two and then just square with my 25 to get five times root two so that is five we've got two simplified let's do another one root ninety six so i'm looking for two numbers at times together to make 96. if you do that you'll get 16 and how many times is 16 going where it goes in six times so the square root of 16 is four so it's four times root six or four root six is the final answer always find the biggest square number that goes in if i'd used four there then i would have had to simplify again at the end you're multiplying sorts so if you've got two numbers with a root and you want to times them together you can just times the numbers under the root so i can just do the square root of 5 times 15 that's the square root of 75 but if you could simplify it you then simplify it so square root of 75 well that's just 25 times 3. square root of 25 is 5 so there we go 5 root 3 is our final answer let's try another one square root of 10 times 12 so that's the square root of 10 times 12 that's 120 so you're looking for a square number if it goes into 120 quite quickly you'll get 94. four's the only square number if it goes into 120 so i can write that as the square root of 4 times the square root of 30. since 4 is the biggest one it goes in i know that root 30 is simplified already square root of 4 is 2. so we've got two fair a and one done dividing starts so if you've got a square root divided by a square root then that's the same as doing one square root with the numbers divided by each other so the square root of 48 divided by 3 well 48 divided by 3 is 16. so we've got the square root of 16 which in this case is just 4. you simplify the end which in this case is a whole square number either and subtracts and such you can only add and subtract thirds if the number under the square root is exactly the same otherwise you can't add them but you can sometimes simplify a sub to make it look the same or both sides so let's have a look at this example with 50 possible eight let's just hit the side root 50 that is 25 times 2 so that gives me 5 root 2. let's do the same thing with root 8 that is 4 times two square root of four is two so that's two root two so this whole sum becomes five root two plus two root two well that's fine five root two and another two two makes seven of them so i've got seven root two in total and we're done with that one okay i'll pass paper question 2014 paper one question eight four eight plus four root ten plus group ninety as a third in its simplest form can't add them we're all simplified so let's start with route 40. so what about 40. well that's just 4 times 10 to 10. notice how that 10 has appeared and we now know that root 10 is already simplified because 4 is the biggest square number it wasn't a 4. and it gave us 10 as an answer so i don't have to try and simplify my good 10. so i'm now going to simplify my root 90 well that's 9 times 10. square root of nine is three so that gives us three root ten so our whole sum simplifies into two root ten plus our four root ten is already there plus an extra 3 10. so adding all of them together 2 plus 4 is 6 plus another 3 is 9 our answer is 9 lots of root 10 and we're done you