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(180^(1/2) +45^(1/2))/135^(1/2)

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(180^(1/2) +45^(1/2))/135^(1/2)  [#permalink]

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New post 25 Apr 2017, 03:08
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (02:04) correct 30% (02:51) wrong based on 189 sessions

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Re: (180^(1/2) +45^(1/2))/135^(1/2)  [#permalink]

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New post 25 Apr 2017, 06:26
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Bunuel wrote:
\(\frac{\sqrt{180}+\sqrt{45}}{\sqrt{135}}\)

A. \(\sqrt{3}\)

B. \(3\sqrt{3}\)

C. \(5\sqrt{3}\)

D. \(3\sqrt{5}\)

E. \(5\sqrt{5}\)


We'll simplify each root by using the rule: √(ab) = (√a)(√b)

√180 = √(36 x 5) = (√36)(√5) = 6√5
√45 = √(9 x 5) = (√9)(√5) = 3√5
√135 = √(9 x 15) = (√9)(√15) = 3√15

So, \(\frac{\sqrt{180}+\sqrt{45}}{\sqrt{135}}\) = (6√5 + 3√5)/(3√15)

= (9√5)/(3√15)
= 3/(√3)

Check the answer choices....not there!
We must rationalize the denominator.
Take 3/(√3) and multiply numerator and denominator by √3 to get: (3√3)/3, which simplifies to √3

Answer:

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Re: (180^(1/2) +45^(1/2))/135^(1/2)  [#permalink]

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New post 25 Apr 2017, 06:33
Why not B. 3/sqrt 3 is in B

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Re: (180^(1/2) +45^(1/2))/135^(1/2)  [#permalink]

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New post 25 Apr 2017, 06:42
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Somnath09 wrote:
Why not B. 3/sqrt 3 is in B

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Here's another way to think of it.
We know that (sqrt 3)(sqrt 3) = 3, so let's replace the numerator, 3, with (sqrt 3)(sqrt 3)

We get: 3/sqrt 3 = (sqrt 3)(sqrt 3)/(sqrt 3) =sqrt 3

Cheers,
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Re: (180^(1/2) +45^(1/2))/135^(1/2)  [#permalink]

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New post 25 Apr 2017, 19:36
Taking \(\sqrt{45}\) common from numerator and denominator
\(\sqrt{45}\)(\(\sqrt{4}\)+1) / \(\sqrt{45}\)*(\(\sqrt{3}\))
(2+1)/\(\sqrt{3}\)
3/\(\sqrt{3}\)
\(\sqrt{3}\)
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Re: (180^(1/2) +45^(1/2))/135^(1/2)  [#permalink]

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New post 28 Apr 2017, 15:15
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1
Bunuel wrote:
\(\frac{\sqrt{180}+\sqrt{45}}{\sqrt{135}}\)

A. \(\sqrt{3}\)

B. \(3\sqrt{3}\)

C. \(5\sqrt{3}\)

D. \(3\sqrt{5}\)

E. \(5\sqrt{5}\)


We can start by simplifying √180, √45, and √135:

√180 = √36 x √5 = 6√5

√45 = √9 x √5 = 3√5

Thus, 6√5 + 3√5 = 9√5.

√135 = √9 x √15 = 3√15

We now have:

(9√5)/(3√15) = 3/√3

Finally, we rationalize the denominator, getting:

(3/√3)(√3/√3) = 3√3/3 = √3

Answer: A
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Re: (180^(1/2) +45^(1/2))/135^(1/2)  [#permalink]

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Re: (180^(1/2) +45^(1/2))/135^(1/2)   [#permalink] 25 Mar 2019, 09:20
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