Discussion Thread

So who likes surds? I always find them confusing can anyone help me?

Surds are basically a simplified root.
for example:
              ___
simplify  \|72         


Now u look for square factors of 72.........36

so you know that 72 can be represented as 36 x 2
      ___             _______
so \|72    =      \|36 x 2
                     ___                  At this point u square root the 36 to get 6.
              =  6\|2     Is a surd as it cannot be simplified anymore.

I have a number of surds questions and i am not sure how to do them can anyone help?

a) how do you subtract mixed surds like 3 Ö7 - Ö28

b) how do you multiply mixed surds like 2Ö3 x Ö6 and Ö10 x 3Ö5 and 5Ö6 x 2Ö3

Hiya Tom,

Do you know the rules for working with surds?

The main rules that you need to know with surds are :-  

Addition and subtraction of surds

aÖb + cÖb = (a + c)Öb
aÖb - cÖb = (a - c)Öb

Multiplication and Division

Öab = Öa × Öb
Ö(a/b) = Öa/Öb

why not try the following work item for a bit more practise on surds
Recurring Decimals and Surds -LETTS

looking at your problems
a) you need to make it so they have the same surd so can you rewrite it into the format aÖb - cÖb

b) you can multiply these together. Don't forget to not lose the Ö when you are doing the multiplication. You can then possibly find square factors and remove them.

I hope that helps have a go and let us know how you got on!

ok I got

a) 3 Ö7 -4Ö7 so -Ö7

b) I just done the first one and got 2Ö18

is that right?

Tom in a) you have forgotten to take the square root of 4 when you take it out side of the root symbol so it should be 3 Ö7 -2Ö7.

In the b) you are on the right track but you can simplify that down more look for square factor of 18 and then simplify it down further

ok cheers I think i have it now so

a) is Ö7

and then for b) I get

2Ö18 = 2Ö(9x2) = 2x3Ö2=6Ö2

I think I can do the rest thanks

You can apply the power to the numerator and denominator independent of each other
                            ____                   _____ 
So it becomes 1 / \|(2^9) which is 1/ \|(2^8*2) as now root of 2^8 is 2^4
                                 _        _     _ 
= 1/(2^4*v2) = 1/(2^4*\|2)  * (\|2 / \|2) multiply top and bottom by root 2
     _             _
= \|2 / 2^5 = \|2 / 32

I hope that all makes sense.