Simplify - square root of 16/144

$- \sqrt{\frac{16}{144}}$

Cancel the common factor of $16$ and $144$ .

Factor $16$ out of $16$ .

$- \sqrt{\frac{16 (1)}{144}}$

Cancel the common factors.

Factor $16$ out of $144$ .

$- \sqrt{\frac{16 \cdot 1}{16 \cdot 9}}$

Cancel the common factor.

$- \sqrt{\frac{16 \cdot 1}{16 \cdot 9}}$

Rewrite the expression.

$- \sqrt{\frac{1}{9}}$

Rewrite $\sqrt{\frac{1}{9}}$ as $\frac{\sqrt{1}}{\sqrt{9}}$ .

$- \frac{\sqrt{1}}{\sqrt{9}}$

Any root of $1$ is $1$ .

$- \frac{1}{\sqrt{9}}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$- \frac{1}{\sqrt{3^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$- \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{3}$

Decimal Form:

$- 0.\overline{3}$