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12^(1/2) + 108^(1/2) + 48^(1/2) =

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12^(1/2) + 108^(1/2) + 48^(1/2) = [#permalink]

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New post 06 Apr 2018, 05:09
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

85% (00:48) correct 15% (01:35) wrong based on 66 sessions

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12^(1/2) + 108^(1/2) + 48^(1/2) = [#permalink]

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New post 06 Apr 2018, 21:20
Bunuel wrote:
\(\sqrt{12} + \sqrt{108} + \sqrt{48} =\)

A. \(12\sqrt{3}\)

B. 24

C. \(12\sqrt{5}\)

D. \(48\sqrt{3}\)

E. \(\sqrt{168}\)

\(\sqrt{12} + \sqrt{108} + \sqrt{48} =\)

Put factors under the radical signs, looking for factors that are perfect squares.
Look also, and first, for a common factor that is NOT a perfect square, one that will remain beneath the radical sign.

Check the answer choices for possible factors that are not perfect squares.
Here, choices are \(\sqrt{3}\), \(\sqrt{5}\), and \(\sqrt{168}\)

5 is not a factor at all. 168 is too great to work with. Ignore.
Try 3 under the radical sign.
Once you divide each number by 3, the remaining factor is a perfect square.

\(\sqrt{3*4} + \sqrt{3*36} + \sqrt{3*16} =\)

\((\sqrt{3}*\sqrt{4}) + (\sqrt{3}*\sqrt{36}) + (\sqrt{3}*\sqrt{16})\)

Take the square roots of the factors that are perfect squares:

\(2\sqrt{3} + 6\sqrt{3} + 4\sqrt{3} =12\sqrt{3}\)

Answer A
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12^(1/2) + 108^(1/2) + 48^(1/2) =   [#permalink] 06 Apr 2018, 21:20
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