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Maths year 11

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Correct. What about something like 12+3\displaystyle \frac{1}{2+\sqrt{3}} ? It would be the same method with a slight twist.

To firstly investigate, think about what happens when you multiply the denominator by 2+32+\sqrt{3} and then see what happens if you multiply it by 232-\sqrt{3}. This may prove to be quite challenging but I believe it would appear at the end of Higher papers. :smile:
(edited 7 years ago)
Reply 1181
Original post by RDKGames
Correct. What about something like 12+3\displaystyle \frac{1}{2+\sqrt{3}} ? It would be the same method with a slight twist. To firstly investigate, think about what happens when you multiply the denominator by 2+32+\sqrt{3} and then see what happens if you multiply it by 232-\sqrt{3}. This may prove to be quite challenging. :smile:


Yeah I get stuck on the expand and simplifying ones



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Reply 1182
Original post by RDKGames
Correct. What about something like 12+3\displaystyle \frac{1}{2+\sqrt{3}} ? It would be the same method with a slight twist. To firstly investigate, think about what happens when you multiply the denominator by 2+32+\sqrt{3} and then see what happens if you multiply it by 232-\sqrt{3}. This may prove to be quite challenging. :smile:


Yeah I get stuck on the expand and simplifying ones
.


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Original post by z_o_e
Yeah I get stuck on the expand and simplifying ones
.


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You expanded correctly (though the last bracket should have a multiplication sign!). Now it's just a matter of collecting the terms. Remember the surd rule: ab=ab\sqrt{a} \cdot \sqrt{b} = \sqrt{a\cdot b} and the fact that you cannot simplify something like 232\sqrt3 any further, so you leave that as it is.
Reply 1184
Original post by RDKGames
You expanded correctly (though the last bracket should have a multiplication sign!). Now it's just a matter of collecting the terms. Remember the surd rule: ab=ab\sqrt{a} \cdot \sqrt{b} = \sqrt{a\cdot b} and the fact that you cannot simplify something like 232\sqrt3 any further, so you leave that as it is.




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Actually, hold on. There is a mistake in your expansions I missed. The last bracket should be 22-\sqrt2 \cdot 2. Look at the arrows coming out for the first bracket, you have 3 from 3\sqrt3 and only 1 from 2\sqrt2 which means you are doing an extra needless calculation which you've already covered. Check it.
Reply 1186
Original post by RDKGames
Actually, hold on. There is a mistake in your expansions I missed. The last bracket should be 22-\sqrt2 \cdot 2. Look at the arrows coming out for the first bracket, you have 3 from 3\sqrt3 and only 1 from 2\sqrt2 which means you are doing an extra needless calculation which you've already covered. Check it.


Did it again

I don't know how to workout the 2nd bracket the one with a negative surd



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Original post by z_o_e
Did it again

I don't know how to workout the 2nd bracket the one with a negative surd



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In the same way you worked out 32\sqrt3 \cdot 2 just, well, it's a negative quantity this time.
Reply 1188
Original post by RDKGames
In the same way you worked out 32\sqrt3 \cdot 2 just, well, it's a negative quantity this time.


Correct?

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Reply 1189
How should I add them now ? :/



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Original post by z_o_e
How should I add them now ? :/



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Yeppp. Add what???
Reply 1191
Original post by RDKGames
Yeppp. Add what???


You know when I have to work out the next step I need to add these right?


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Original post by z_o_e
You know when I have to work out the next step I need to add these right?


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Yeah you would only add them if they shared any common terms. In this case they are all individual so you don't.

If there was something like 3+1+732\sqrt3 + 1 + 7\sqrt3 - \sqrt2 then you can add the 3\sqrt3 and 737\sqrt3 (which would gives you 838\sqrt3) because 3\sqrt3 is a common term amongst those two numbers.
(edited 7 years ago)
Reply 1193
Oh okay :smile:

So what do I do next?

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Original post by z_o_e
Oh okay :smile:

So what do I do next?

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You can leave the answer as it is since you cannot simplify it any further.

Have a go at the question I've proposed earlier.
Reply 1195
Original post by RDKGames
You can leave the answer as it is since you cannot simplify it any further.

Have a go at the question I've proposed earlier.


Yep I will can I have a bit of an explanation to how to do that whilst I do another example to this x

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Reply 1196
Original post by RDKGames
You can leave the answer as it is since you cannot simplify it any further.

Have a go at the question I've proposed earlier.


What do I do after this step?


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Original post by z_o_e
Yep I will can I have a bit of an explanation to how to do that whilst I do another example to this x

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Well the explanation would come from you attempting to rationalise the denominator there by getting rid off the 3\sqrt3.

Hint:

Spoiler

(edited 7 years ago)
Original post by z_o_e
What do I do after this step?


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You got the part with 245+182\sqrt{45} + 18 right and you know that 45=35\sqrt{45}=3\sqrt5 from what you've shown. You can use this replace the 45\sqrt{45} in the original answer.
Reply 1199
Original post by RDKGames
Well the explanation would come from you attempting to rationalise the denominator there by getting rid off the 3\sqrt3.

Hint:

Spoiler



Here


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