This was our first week back at school after a long summer. We started off with a review on types of numbers and then we expanded to a new concept which is entire radicals and mixed radicals. For example √3 is an entire radical while 5√3 is a mixed radical. The difference is an entire radical has a coefficient that is just 1 so we don’t write it while a mixed radical has a coefficient other than 1.
In this blog post I will explain the two ways of getting a mixed fraction.
Way 1
Step 1: 
So as you can see we are using square root of 32. I’m going to think what two number multiply to have a product of 32 while one being a perfect square.
Step 2: 
In this step I showed separately square root of 8 multiplied by square root of 8. I find it easier to put the perfect square in front because I’m going to be pulling that one out anyway.
Step 3: 
In this final step you can see I pulled out a 2 in front of square root of 8, I got that 2 because I square rooted the 4 which gives me 2 and because 8 has no square root you just leave it.
This way of doing it is fast and easy and works really well when you are working with smaller numbers. I find when you are using bigger number this next way is much easier and saves me time.
Way 2
Step 1: 
So in this example I’m starting with a bigger number. As you can see I broke it down into a number tree like we learnt how to last year, getting all the prime factors.
Step 2: 
So in this step I took all the prime factors and put them into a big square root. As you can see I circled all the pairs of numbers. Those are the numbers I’m going to pull out and put out in front. So I would go 2×2 which 4 then square rooted is 2 and same thing for the 3’s, 3×3=9 square rooted is 3 and then I am going to multiply 2 and 3 which is going to give me 6.
Step 3: 
This is the final step. I explained how to get the 6 but where did the 10 come from? If you look at our big square root the two numbers left over that weren’t in a pair were 2 and 5. I am going to multiply them together and that’s where the 10 comes from. And that’s it!
I find both of these methods useful, depending on how big the number is depends on what method i am going to use!