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# Sqare Root Property

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Manager
Joined: 30 May 2008
Posts: 74

Kudos [?]: 146 [0], given: 26

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09 Apr 2012, 09:33
([square_root 10] + [square_root 10][/square_root 2]) ^2

why can't it be ([square_root 10][/square root 2)^2 + ([square_root 10][/square root 2)^2

Kudos [?]: 146 [0], given: 26

Manager
Joined: 30 May 2008
Posts: 74

Kudos [?]: 146 [0], given: 26

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09 Apr 2012, 10:08
Thanks for the explanation! I needed that too

Maybe this will help: (sqr = square root)

[sqr 10 + sqr 10 / sqr 2 ] ^ 2

Can you explain why below is incorrect?

=> [sqr 10 / sqr 2]^2 + [sqr 10 / sqr 2]^2

=> 5 + 5 = 10

but the OA is 20

Kudos [?]: 146 [0], given: 26

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7738

Kudos [?]: 17815 [0], given: 235

Location: Pune, India

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11 Apr 2012, 10:26
catty2004 wrote:
([square_root 10] + [square_root 10][/square_root 2]) ^2

why can't it be ([square_root 10][/square root 2)^2 + ([square_root 10][/square root 2)^2

Go to algebra section of khanacademy.org and check out videos on 'Simplifying Radicals' there. They should help you understand how to deal with such questions.
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Kudos [?]: 17815 [0], given: 235

Manager
Joined: 28 Sep 2011
Posts: 68

Kudos [?]: 33 [0], given: 10

Location: United States
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11 Apr 2012, 11:42
Either I'm reading this wrong or I need help with this also.

The question is [sqr 10 + sqr 10 / sqr 2 ] ^ 2

I'm reading this as (sqrt(10) + sqrt(5))^2 (The denominator is only under the second sqrt(10))

After factoring I'm getting 15 + 2sqrt(50)

Now if the denominator (sqrt(2)) is spanned across the entire numerator the problem becomes (2sqrt(5))^2 = 20

Kudos [?]: 33 [0], given: 10

Math Expert
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132780 [1], given: 12372

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11 Apr 2012, 11:53
1
KUDOS
Expert's post
ashish8 wrote:
Either I'm reading this wrong or I need help with this also.

The question is [sqr 10 + sqr 10 / sqr 2 ] ^ 2

I'm reading this as (sqrt(10) + sqrt(5))^2 (The denominator is only under the second sqrt(10))

After factoring I'm getting 15 + 2sqrt(50)

Now if the denominator (sqrt(2)) is spanned across the entire numerator the problem becomes (2sqrt(5))^2 = 20

Here is the question with a solution; $$(\frac{\sqrt{10}+\sqrt{10}}{\sqrt{2}})^2=(\frac{2\sqrt{10}}{\sqrt{2}})^2=\frac{4*10}{2}=20$$.
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Kudos [?]: 132780 [1], given: 12372

Re: Sqare Root Property   [#permalink] 11 Apr 2012, 11:53
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