The answer is [tex]2 \sqrt{3} [/tex]
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 [tex] \sqrt{12} [/tex] into [tex] \sqrt{2 *2*3} [/tex]
Let's continue to simplify:
[tex] \sqrt{2^2*3} [/tex]..........................combine [tex]2*2[/tex] into [tex] 2^{2} [/tex]
[tex] 2\sqrt{3} [/tex]................................[tex] \sqrt{2^2} [/tex] 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! :)
