Solve (-1/2)^2-sqrt{54}-1

$$( - \frac { 1 } { 2 } ) ^ { 2 } - \sqrt { 54 } - 1$$

Evaluate

$$-3\sqrt{6}-\frac{3}{4}\approx -8.098469228$$

Solution Steps

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

$$\frac{1}{4}-\sqrt{54}-1$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$\frac{1}{4}-3\sqrt{6}-1$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{1}{4}-3\sqrt{6}-\frac{4}{4}$$

Since \frac{1}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-4}{4}-3\sqrt{6}$$

Subtract 4 from 1 to get -3.

$$-\frac{3}{4}-3\sqrt{6}$$

Factor

$$\frac{3 {(-4 \sqrt{6} - 1)}}{4} = -8.098469228349533$$