How do you find the simplest radical form of 12?

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Answer 1 · 2018-03-25T02:37:12

The simplified radical form of $\sqrt{12}$ $sqrt12$ is $2 \sqrt{3}$ $2sqrt3$ .

We need to utilize these two radical rules:

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ $sqrt(color(red)a*color(blue)b)=sqrtcolor(red)a*sqrtcolor(blue)b$

$\sqrt{a^{2}} = a$ $color(red)sqrt(color(black)a^2)=a$

To solve our problem, first, factor $12$ $12$ into its prime factorization, then apply those two rules. Here's what that will look like:

$= \sqrt{12}$ $color(white)=sqrt12$

$= \sqrt{4 \cdot 3}$ $=sqrt(color(red)4*color(blue)3)$

$= \sqrt{2 \cdot 2 \cdot 3}$ $=sqrt(color(red)(2*2)*color(blue)3)$

$= \sqrt{2^{2} \cdot 3}$ $=sqrt(color(red)(2^2)*color(blue)3)$

$= \sqrt{2^{2}} \cdot \sqrt{3}$ $=sqrtcolor(red)(2^2)*sqrtcolor(blue)3$

$= 2 \cdot \sqrt{3}$ $=color(red)2*sqrtcolor(blue)3$

$= 2 \sqrt{3}$ $=color(red)2sqrtcolor(blue)3$

That's as simplified as it gets. Hope this helped!