Question

Simplify the expression √12

Answer 1

The answer is $2 \sqrt{3}$

The reason this is so is because when we are looking to simplify an expression such as this we have to break the radicand up into a product of known factors. Here are the factors of 12:

1, 2, 3, 4, 6, 12

In this case, what is ideal is if we can find a factor of 12 that is a perfect square.

A perfect square is any number that is equal to any number being multiplied by itself. Some examples are:

1 × 1 = 1 , 1 is a perfect square
2 × 2 = 4, 4 is a perfect square
3 × 3 = 9, 9 is a perfect square
4 × 4 = 16, 16 is a perfect square
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In the factors of 12, we have 4, which can be broken down into 2 × 2

So, we could change $\sqrt{12}$ into $\sqrt{2 *2*3}$

Let's continue to simplify:

$\sqrt{2^2*3}$..........................combine $2*2$ into $2^{2}$

$2\sqrt{3}$................................$\sqrt{2^2}$ is redundant and is equal to 2, so your left with 3 under the radical since it cannot be simplified any more

And that's your answer and how you get it! I hope this helped and have an amazing rest of your day! Feel free to contact me if you have anymore questions and I will do my best to help! :)

Answer 2

12 can be broken into 4*3 or 2^2 *3
so √12 can be 2√3