Simplify square root of 12/(b^2)

$\sqrt{\frac{12}{b^{2}}}$

Step 1

Rewrite $\frac{12}{b^{2}}$ as ${(\frac{2}{b})}^{2} \cdot 3$ .

Factor the perfect power $2^{2}$ out of $12$ .

$\sqrt{\frac{2^{2} \cdot 3}{b^{2}}}$

Factor the perfect power $b^{2}$ out of $b^{2}$ .

$\sqrt{\frac{2^{2} \cdot 3}{b^{2} \cdot 1}}$

Rearrange the fraction $\frac{2^{2} \cdot 3}{b^{2} \cdot 1}$ .

$\sqrt{{(\frac{2}{b})}^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$\frac{2}{b} \sqrt{3}$

Step 3

Combine $\frac{2}{b}$ and $\sqrt{3}$ .

$\frac{2 \sqrt{3}}{b}$