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

Question

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

A.  12\sqrt{3}

B. 24

C.  12\sqrt{5}

D.  48\sqrt{3}

E.  \sqrt{168}

generis · Answer

\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

BelalHossain046 · Answer

Convert every term in Root (12).
First term: Root 12
2nd term: Root 48= Root(4*12)=2 Root 12

3rd term: Root 109=Root (9*12)=3 Root 12.

So, 1st term + 2nd term +3rd term 
=6 Root 12 (since no such thing available in options, do further steps.
= 6 * Root (4*3)
=6*2*Root 3
=12 ROOT 3.
A is my answer.

Posted from my mobile device

Shrey9 · Answer

The answer options are varied, which is a hint, once we find the common factor, we can quickly guess and move on

solving the biggest value first so we'll know the maximum value out of the 3 terms. 
 \sqrt{108}  =
 \sqrt{36*3} 
 6\sqrt{3} ,

as we can see A is the smaller of the two answers with  \sqrt{3} .. we can mark A right away..

there's no chance that we will touch 48 outside square root, as biggest number outside square root is 6

also you can guess that  \sqrt{12}  will be somewhat closer to 3
and  \sqrt{48}  will be closer to 7
and as we have  \sqrt{3}  as common, so these 2 values will be les than 3 and 7 
6+7+3 = 16, closest one is  12\sqrt{3} 
so A is pretty much right on this one

CareerGeek · Answer

\sqrt{12} + \sqrt{108} + \sqrt{48} 
-->  \sqrt{4*3} + \sqrt{36*3} + \sqrt{16*3} 
-->  2\sqrt{3} + 6\sqrt{3} + 4\sqrt{3} 
-->  12\sqrt{3}

IMO Option A

Pls Hit Kudos if you like the solution

ScottTargetTestPrep · Answer

Simplifying and combining, we have:

√4 x √3 + √36 x √3 + √16 x √3

2√3 + 6√3 + 4√3 = 12√3

Answer: A

bumpbot · Answer

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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) =

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