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Maths

Hi. How would you write (2+square root of 5)^(2) in the form
a+b x (square root of 5).

So far I have got that 2^(2) = 4 and root 5 squared = root 25 which is 5. Is that right?
I don't know where to go from here.
2+2 is 4, minus 1 that's 3. Quick maths.
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Maths1210
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Original post by RenéDescartes
2+2 is 4, minus 1 that's 3. Quick maths.


Very funny.
Original post by Maths1210
Very funny.


Everyday mans on the block. Smoke trees.
Reply 4
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number0
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Remember (A + B)^2 = A^2 + 2AB + B^2

It does not equal A^ + B^2
You can't square them individually, its a bracket multiplying a bracket so (2+sqrt5)(2+sqrt5)=??
working with roots can be difficult and confusing, for some. For me, the best way to do this question is to treat is as algebra; imagine (or replace if you need visual help) the /5 with x (or any other algebra term). Firstly you have to get rid of the (^2) so:

( key: / = square root) :

(2+/5)^2 -> (2+/5) x (2+/5) (expand the question so you can visually see what you have to do)

(2+/5) x (2+/5) (once you are comfortable with these types of questions, you can skip some steps like visually expanding although examiners sometimes want to see how you do it)

= (2x2)+(2x/5)+(/5x2)+(/5x/5) (this is multiplying out the brackets)

= 4+ 2/5 + 2/5+ 5 (working out inside the brackets)

= 9 +2/5 +2/5 (simplify by adding likely terms)

=9+ 4/5 (imagine they asked to add 2x+2x, you would get 4x)

so a=9 and b=4.

If there's anything you didn't understand, write back. Hope this helps!
(edited 6 years ago)
Reply 7
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Original post by number0
Remember (A + B)^2 = A^2 + 2AB + B^2

It does not equal A^ + B^2


I don't know what you mean by 2AB. Could you explain that please?
Original post by Maths1210
I don't know what you mean by 2AB. Could you explain that please?


it means 2 x A x B. The x means multiply.
Reply 9
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Maths1210
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Original post by evelina s
working with roots can be difficult and confusing, for some. For me, the best way to do this question is to treat is as algebra; imagine (or replace if you need visual help) the /5 with x (or any other algebra term). Firstly you have to get rid of the (^2) so:

( key: / = square root) :

(2+/5)^2 -> (2+/5) x (2+/5) (expand the question so you can visually see what you have to do)

(2+/5) x (2+/5) (once you are comfortable with these types of questions, you can skip some steps like visually expanding although examiners sometimes want to see how you do it)

= (2x2)+(2x/5)+(/5x2)+(/5x/5) (this is multiplying out the brackets)

= 4+ 2/5 + 2/5+ 5 (working out inside the brackets)

= 9 +2/5 +2/5 (simplify by adding likely terms)

=9+ 4/5 (imagine they asked to add 2x+2x, you would get 4x)

so a=9 and b=4.

If there's anything you didn't understand, write back. Hope this helps!


Thank you this really helped. I always forget to put it into brackets.

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