Solve sqrt{2*(-5/2)^-2-2^-2}

$$\sqrt { 2 \cdot ( - \frac { 5 } { 2 } ) ^ { - 2 } - 2 ^ { - 2 } }$$

Evaluate

$$\frac{\sqrt{7}}{10}\approx 0.264575131$$

Solution Steps

Calculate -\frac{5}{2} to the power of -2 and get \frac{4}{25}.

$$\sqrt{2\times \frac{4}{25}-2^{-2}}$$

Multiply 2 and \frac{4}{25} to get \frac{8}{25}.

$$\sqrt{\frac{8}{25}-2^{-2}}$$

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

$$\sqrt{\frac{8}{25}-\frac{1}{4}}$$

Subtract \frac{1}{4} from \frac{8}{25} to get \frac{7}{100}.

$$\sqrt{\frac{7}{100}}$$

Rewrite the square root of the division \sqrt{\frac{7}{100}} as the division of square roots \frac{\sqrt{7}}{\sqrt{100}}.

$$\frac{\sqrt{7}}{\sqrt{100}}$$

Calculate the square root of 100 and get 10.

$$\frac{\sqrt{7}}{10}$$