Put the following in order of size, smallest first: 8/sqrt3, sqrt6*sqrt2, sqrt48-sqrt27
First part of the question is to recognise that these are surds and we will need to simplify them. Then it is asking to place the values from smallest to highest. In order to simplify the surds we have to find a common sqrt. In this case it is sqrt3.
For the first value: 8/sqrt3 we have to times the bottom and top by sqrt3 because we are not allowed to have a sqrt as a denominator. A sqrt times by itself we just get the number, which is 3. Then the top, (which is also times by sqrt3) becomes 8sqrt3. Thus the end result is 8sqrt3/3
For the Second Value: sqrt6sqrt2. Now, here we have to simplify the surd sqrt6. This can be split up into sqrt3 and sqrt2. Surds have to be in their most simple form and try to get sqrt's into prime numbers, whereby they can no longer be divisible by any number. As a result of this we now have sqrt3sqrt2sqrt2. Sqrt2sqrt2 becomes sqrt4. As 4 is a square number (A number times itself gives a square value) as 22 = 4. We now have the end result of 2sqrt3.
For the Third Value: sqrt48 - sqrt27. As we are using a common sqrt root of 3 for all three values. We have to find out how these numbers can be divided by 3. For example, sqrt48 divided by 3 is 16. 16 is a squared number so we now have the value 4sqrt3. For sqrt27, 27 divided by 3 is 9, also a squared number, so the result is 3sqrt3. Thus it becomes 4sqrt3 - 3sqrt3 = 1sqrt3
Now to answer the question we have to put the values from smallest to highest.The smallest is sqrt3The middle is 2sqrt3The highest is 8sqrt3/3 (We can check using a calculator if one is allowed)
