Question

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

Answer 1

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! (:

Answer 2

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.