Question

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

Answer 1

Answer:

Yes; $2\sqrt{3} .$ is correct.

Step-by-step 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 $\sqrt{2^2\cdot \:3}$. That can be written as $\sqrt{2^2}\sqrt{3}$.

$\sqrt{2^{2}} = 2$.

$2 \: \cdot \: \sqrt{3} = 2\sqrt{3}.$

Thusly, you are correct, it is $2\sqrt{3} .$

Hope this helps! (:

Answer 2

Answer: Yes, it is $2\sqrt{3}$

Step-by-step explanation:

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

$\sqrt{12}=\sqrt{4*3} =\sqrt{2*2*3}$

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

$2\sqrt{3}$,

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.