Solve -1-sqrt{16/1-1/25}

$$- 1 - \sqrt { \frac { 16 } { 1 } - \frac { 1 } { 25 } }$$

Evaluate

$$-\frac{\sqrt{399}}{5}-1\approx -4.994996871$$

Short Solution Steps

Anything divided by one gives itself.

$$-1-\sqrt{16-\frac{1}{25}}$$

Convert 16 to fraction \frac{400}{25}.

$$-1-\sqrt{\frac{400}{25}-\frac{1}{25}}$$

Since \frac{400}{25} and \frac{1}{25} have the same denominator, subtract them by subtracting their numerators.

$$-1-\sqrt{\frac{400-1}{25}}$$

Subtract 1 from 400 to get 399.

$$-1-\sqrt{\frac{399}{25}}$$

Rewrite the square root of the division \sqrt{\frac{399}{25}} as the division of square roots \frac{\sqrt{399}}{\sqrt{25}}.

$$-1-\frac{\sqrt{399}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$-1-\frac{\sqrt{399}}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -1 times \frac{5}{5}.

$$-\frac{5}{5}-\frac{\sqrt{399}}{5}$$

Since -\frac{5}{5} and \frac{\sqrt{399}}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-\sqrt{399}}{5}$$

Factor

$$\frac{-\sqrt{399} - 5}{5} = -4.994996871087635$$