# Help with a mathematics question - rationalising

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#1
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

0
1 week ago
#2
(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

Use the difference of two squares on the denominator.
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#3
(Original post by mqb2766)
Use the difference of two squares on the denominator.
Thing is they're squared so I'm unsure of how to use the difference of two squares
0
1 week ago
#4
(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
0
1 week ago
#5
(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).
1
1 week ago
#6
(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

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

1
#7
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
0
1 week ago
#8
(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:

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

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#9
(Original post by RogerOxon)
You don't to solve this question. What you have done, so far, is correct.

The difference of squares is:

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

Ohh tysm

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