Evaluate - square root of 100/81

$- \sqrt{\frac{100}{81}}$

Rewrite $\sqrt{\frac{100}{81}}$ as $\frac{\sqrt{100}}{\sqrt{81}}$ .

$- \frac{\sqrt{100}}{\sqrt{81}}$

Simplify the numerator.

Rewrite $100$ as $10^{2}$ .

$- \frac{\sqrt{10^{2}}}{\sqrt{81}}$

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

$- \frac{10}{\sqrt{81}}$

Simplify the denominator.

Rewrite $81$ as $9^{2}$ .

$- \frac{10}{\sqrt{9^{2}}}$

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

$- \frac{10}{9}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{10}{9}$

Decimal Form:

$- 1.\overline{1}$

Mixed Number Form:

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