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What is the square root of 12 simplified? Is it 2 times the square root of 3?

User Leonidv
by
7.6k points

2 Answers

4 votes

Answer:

Yes;
2√(3) . is correct.

Explanation:

Remember that to find the simplified radical you must first break down the number given into its prime factors.

prime factorization of 12:
2^2\cdot \:3.

So we have
√(2^2\cdot \:3). That can be written as
√(2^2)√(3).


\sqrt{2^(2)} = 2.


2 \: \cdot \: √(3) = 2√(3).

Thusly, you are correct, it is
2√(3) .

Hope this helps! (:

User Stvnrlly
by
6.8k points
5 votes

Answer: Yes, it is
2√(3)

Explanation:

To simplify square roots, you can factor the number inside the square root into its lowest common denominators.


√(12)=√(4*3) =√(2*2*3)

Any value that appears twice can be "taken out" of the square root and moved to the left of it:


2√(3),

What you are doing is essentially taking the square root of 4 and the square root of 3. Because the square root of 4 can be simplified, and the square root of 3 cannot, this is the most simplified version of the expression we can reach.

User Sagar Gupta
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7.7k points