Solve 1-sqrt{3-2^-4}

$$1 - \sqrt { 3 - 2 ^ { - 4 } }$$

Evaluate

$$-\frac{\sqrt{47}}{4}+1\approx -0.71391365$$

Short Solution Steps

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$1-\sqrt{3-\frac{1}{16}}$$

Subtract \frac{1}{16} from 3 to get \frac{47}{16}.

$$1-\sqrt{\frac{47}{16}}$$

Rewrite the square root of the division \sqrt{\frac{47}{16}} as the division of square roots \frac{\sqrt{47}}{\sqrt{16}}.

$$1-\frac{\sqrt{47}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$1-\frac{\sqrt{47}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4}{4}.

$$\frac{4}{4}-\frac{\sqrt{47}}{4}$$

Since \frac{4}{4} and \frac{\sqrt{47}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-\sqrt{47}}{4}$$

Factor

$$\frac{4 - \sqrt{47}}{4} = -0.713913650100261$$