Help with a mathematics question - rationalising

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BerrySpecial
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#1
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I'm supposed to rationalise this question as follows, but I'm unsure of how to do it
Could anyone help me with the method?

12√a
--------------------------
(√a + 2)² - (√a - 2)²

I got the answer 12√a but I'm pretty sure it's not correct

Thanks in advance
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mqb2766
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(Original post by BerrySpecial)
I'm supposed to rationalise this question as follows, but I'm unsure of how to do it
Could anyone help me with the method?

12√a
--------------------------
(√a + 2)² - (√a - 2)²

I got the answer 12√a but I'm pretty sure it's not correct

Thanks in advance
Use the difference of two squares on the denominator.
Upload your working if problems.
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BerrySpecial
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(Original post by mqb2766)
Use the difference of two squares on the denominator.
Upload your working if problems.
Thing is they're squared so I'm unsure of how to use the difference of two squares
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mqb2766
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(Original post by BerrySpecial)
Thing is they're squared so I'm unsure of how to use the difference of two squares
The denominator is the difference of two squares. Use the well known factorization. Things obviously cancel.

You'd get the same result of you expanded and simplified.
Last edited by mqb2766; 1 week ago
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DFranklin
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(Original post by BerrySpecial)
I got the answer 12√a but I'm pretty sure it's not correct
Aside from the other advice you've been given, note that it's fairly easy to check if your answer makes sense for particular values of a. (in this case, choosing a to be a perfect square, e.g. 1 or 4 is going to be very easy to check).
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RogerOxon
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(Original post by BerrySpecial)
I'm supposed to rationalise this question as follows, but I'm unsure of how to do it
Could anyone help me with the method?

12√a
--------------------------
(√a + 2)² - (√a - 2)²

I got the answer 12√a but I'm pretty sure it's not correct

Thanks in advance
You can either see the difference of two squares (denominator), or just multiply it out.

Can you post your working? (Your answer is incorrect)
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BerrySpecial
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I've successfully figured out how to do the expansion brackets

12√a
----------
(a+4√a+4)-(a-4√a+4)

= 12√a
----------
8√a

But I can't for the life of me figure out how to find the difference between squares which I need to do
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RogerOxon
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(Original post by BerrySpecial)
I've successfully figured out how to do the expansion brackets

12√a
----------
(a+4√a+4)-(a-4√a+4)

= 12√a
----------
8√a

But I can't for the life of me figure out how to find the difference between squares which I need to do
You don't to solve this question. What you have done, so far, is correct.

The difference of squares is:

a^2-b^2=(a-b)(a+b)

Applying that here is just a short-cut (although not that much of one):

(\sqrt{a}+2)^2-(\sqrt{a}-2)^2=(\sqrt{a}+2-(\sqrt{a}-2))(\sqrt{a}+2+\sqrt{a}-2)=4(2\sqrt{a})=8\sqrt{a}
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BerrySpecial
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(Original post by RogerOxon)
You don't to solve this question. What you have done, so far, is correct.

The difference of squares is:

a^2-b^2=(a-b)(a+b)

Applying that here is just a short-cut (although not that much of one):

(\sqrt{a}+2)^2-(\sqrt{a}-2)^2=(\sqrt{a}+2-(\sqrt{a}-2))(\sqrt{a}+2+\sqrt{a}-2)=4(2\sqrt{a})=8\sqrt{a}
Ohh tysm

I simply failed to realise that (√a+2)^ is one "number" so to say in the a^ - b^
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