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# Solve this root

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Manager
Joined: 25 May 2009
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Concentration: Finance
GMAT Date: 12-16-2011

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01 Jul 2009, 11:08
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Solve : $$(sqrt(n+1))^2$$

Can someone help me solve this root? Please show work. Thanks.

Kudos [?]: 149 [0], given: 2

GMAT Club team member
Joined: 16 Mar 2009
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Location: Bologna, Italy

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01 Jul 2009, 16:25

Kudos [?]: 996 [0], given: 19

Manager
Joined: 25 May 2009
Posts: 142

Kudos [?]: 149 [0], given: 2

Concentration: Finance
GMAT Date: 12-16-2011

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02 Jul 2009, 05:07

Kudos [?]: 149 [0], given: 2

GMAT Club team member
Joined: 16 Mar 2009
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Kudos [?]: 996 [0], given: 19

Location: Bologna, Italy

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03 Jul 2009, 07:30
I3igDmsu wrote:

sorry I didn't have any middle steps ... it kind of popped out of my head...

$$(\sqrt{n+1})^2 = n+1,$$ where n+1<0, has no solution, for real numbers (cuz $$\sqrt{n} = n^{1/2},$$ where n is a positive real number... so $$((n+1)^{1/2})^2 = (n+1)^{{1/2*2}} =n+1$$)
BUT
$$(\sqrt{n+1})^2 = |n+1|$$ for complex numbers.

I guess you would need someone with degree in math to provide more insight to why it is like that, I'm not that good ))
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Kudos [?]: 996 [0], given: 19

Manager
Joined: 25 May 2009
Posts: 142

Kudos [?]: 149 [0], given: 2

Concentration: Finance
GMAT Date: 12-16-2011

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05 Jul 2009, 20:08
I was looking to simplify the equation above, rather than solve. Can you use the FOIL method here? I guess what I am getting at is if you have an expression under a root and that expression is squared, then do you FOIL out the two expressions? How do you FOIL with roots?

Kudos [?]: 149 [0], given: 2

GMAT Club team member
Joined: 16 Mar 2009
Posts: 115

Kudos [?]: 996 [0], given: 19

Location: Bologna, Italy

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06 Jul 2009, 05:16
I3igDmsu wrote:
Can you use the FOIL method here? I guess what I am getting at is if you have an expression under a root and that expression is squared. Do you FOIL out the two expressions? How do you do it with roots?

You are not making fun of me, are you?

I will suppose that not and will respond. You mean put it this way $$(\sqrt{n+1})(\sqrt{n+1})$$?
No you can't use FOIL because both terms are under one root. You could have used FOIL if it would have been $$(\sqrt{n}+1)^2 =(\sqrt{n}+1)(\sqrt{n}+1)$$ , but even in that case it would be more logical to use perfect square binomial identity - $$(a+b)^2 = a^2+2ab+b^2$$ (Note: you really have to know basic polynomial identities. Make sure you know the answer to these - $$(a \pm b)^2 = ? a^2-b^2=?$$ and maybe $$a^3 \pm b^3=? (a \pm b)^3 =?$$)

BUT in your case, as I said $$(\sqrt{n+1})^2 = ((n+1)^{1/2})^2$$ Note the brackets. You can't use FOIL because of the priority of the operations first you have too take the root (put to the 1/2 power) then square (multiply the brackets)....
To tickle your mind (or maybe to confuse you, so may disregard this part) I could abstractly show this in terms of a function of higher order... like $$f(x) = n+1, g(x) = \sqrt{x}, g(f(x)) = \sqrt{f(x)};$$ agh never mind I will make it overly complicated.. I tried to show that while solving smth it really helps me to make an abstraction i.e. treat some polynomial as one unknown variable to see what operations I have to do with it...

@ramiy make sure you don't confuse this $$(\sqrt{n+1})^2$$ with $$\sqrt{(n+1)^2}$$
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Re: Solve this root   [#permalink] 06 Jul 2009, 05:16
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