Maths year 11

I corrected them in red pen.


Posted from TSR Mobile

yup that's the correct.

I got the rules of rationalising but I don't get the rest you sent on top...

I

Posted from TSR Mobile

Just note that they aren't the rules for rationalising surds, they ARE the rules for surds.



Okay, you can't divide by a surd, well you can, but it's a pain to deal with so when we have a fraction with a surd in the denominator we have to rationalise it - this means to essentially get rid of the surd.


There are two ways:

When you have a surd alone on the bottom e.g.


1/√7 - To rationalise it we just multiply by √7, this will cancel out the surd on the denominator because √7*√7 = 7 and what we do to the bottom we must do to the top...


So we multiply by √7 to get is 1/√7 * √7/√7

Which in turn gives us √7/7 - which is the final answer



Now something more complicated:


(1+√3)(/5-√7)

To get rid of the surd in the denominator we cannot just multiply by √7 this time because while the √7 would cancel out, we'd also get a 5√7


To get rid of the surd we can use a theory if you will called the difference of two squares, if we have let's say (a+b)(a-b) What we end up with is a^2-b^2

notice how there is no ab - this is because they cancel out.


Lets apply it to the sum : (1+√3)/(5-√7)


and focus on the denominator 5-√7 the [I forgot the word for it, but there is a word for it] would be 5+√7 - we just changed the signs


and then we multiply top and bottom by it

(1+√3)(5+√7)/(5-√7)(5+√7)


Multiply out the brackets: (5+√7+5√3+√21)/(25+5√7-5√7-49)


Cleaning that up to get: (5+√7+5√3+√21)/-24

And that would be the final answer.


Sorry If I haven't explained it very well; you're probably better watching a youtube video on rationalising the denominator.

How's this?



Posted from TSR Mobile

Yup!

Yass got it ♥

Wb this one you showed?

So how should I cancel them out. Didn't understand the cancelling bit out.



Posted from TSR Mobile

My example probably wasn't the best since the final answer is VERY mess and you'd never get something looking like that in the exam.


Essentially switch the sign around so it's a (5+√7) then multiply.


Once you expand the brackets the √7 will cancel out.

This?



Posted from TSR Mobile

Like I said; you'd never get an actual question this messy.

Yeah ill move on to another question.
What about these

So I expand it first.


But how do I do 2 surd 7



Posted from TSR Mobile

Multiply out as you normally would, 2√7 just another number.






If you're multiply a surd by 2√7 then you multiply it by the 7 part, if you're multiply a normal integer you multiply the 2 part.

carful, It's 4 multiply by negative 2√7


So you'd have (4*6)+(4*-2√7)+(-√7*6)+(-√7*-2√7)

No,


24 - 8√7 - 6√7+14

= 38 - 14√7

I got this *

I'm so tired of this now finding it hard



Posted from TSR Mobile

Heya, my end of year exam is coming up and I'm doing higher and I'm getting D's I'm currently in year 10 and I know I can do better if I revise. Is anyone else willing to help me with a few questions ?

No, you already had the final answer. You can't simplify the 48 as it's not in the square root.

Like I said; you'd never get an actual question this messy.