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# Maths year 11

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1. (Original post by z_o_e)
I corrected them in red pen.

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yup that's the correct.
2. (Original post by 34908seikj)
yup that's the correct.
I got the rules of rationalising but I don't get the rest you sent on top...

I

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3. (Original post by z_o_e)
I got the rules of rationalising but I don't get the rest you sent on top...

I

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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.
4. (Original post by 34908seikj)
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?

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5. (Original post by z_o_e)
How's this?

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Yup!
6. (Original post by 34908seikj)
Yup!
Yass got it ♥

Wb this one you showed?

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

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7. (Original post by z_o_e)
Yass got it ♥

Wb this one you showed?

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

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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.
8. (Original post by 34908seikj)
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?

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9. Like I said; you'd never get an actual question this messy.
Spoiler:
Show

10. (Original post by 34908seikj)
Like I said; you'd never get an actual question this messy.
Spoiler:
Show

Yeah ill move on to another question.

So I expand it first.

But how do I do 2 surd 7

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11. (Original post by z_o_e)
Yeah ill move on to another question.

So I expand it first.

But how do I do 2 surd 7

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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.
12. (Original post by 34908seikj)
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.

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

So you'd have (4*6)+(4*-2√7)+(-√7*6)+(-√7*-2√7)
14. (Original post by 34908seikj)
carful, It's 4 multiply by negative 2√7

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

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15. No,

24 - 8√7 - 6√7+14

= 38 - 14√7
16. (Original post by 34908seikj)
No,

24 - 8√7 - 6√7+14

= 38 - 14√7
I got this *

I'm so tired of this now finding it hard

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17. (Original post by z_o_e)
I got this *

I'm so tired of this now finding it hard

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No, you already had the final answer. You can't simplify the 48 as it's not in the square root.
18. (Original post by z_o_e)
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 ?
My saviour for Maths GCSE was AchieveMaths on youtube. His videos are completely free and if you watch all his videos he goes through 10 past papers and explains each question thoroughly. It gave me soo much confidence and certainty that I would do well in the exam, I would definitely recommend it to you!
19. (Original post by 34908seikj)
No, you already had the final answer. You can't simplify the 48 as it's not in the square root.
I'm going to carry on with this tomorrow I have no hope today think I did enough today.

Including trigonometry, pythagoras and introduction to surds

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20. (Original post by 34908seikj)
Like I said; you'd never get an actual question this messy.
Spoiler:
Show

It should be -7 on the denominator for .
So answer should be I believe.

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