Solve sqrt{3^2-(frac{1}5^2)^2}

$$\sqrt { 3 ^ { 2 } - ( \frac { 1 } { 5 } ^ { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{2\sqrt{1406}}{25}\approx 2.999733321$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\sqrt{3^{2}-\left(\frac{1}{5}\right)^{4}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9-\left(\frac{1}{5}\right)^{4}}$$

Calculate \frac{1}{5} to the power of 4 and get \frac{1}{625}.

$$\sqrt{9-\frac{1}{625}}$$

Subtract \frac{1}{625} from 9 to get \frac{5624}{625}.

$$\sqrt{\frac{5624}{625}}$$

Rewrite the square root of the division \sqrt{\frac{5624}{625}} as the division of square roots \frac{\sqrt{5624}}{\sqrt{625}}.

$$\frac{\sqrt{5624}}{\sqrt{625}}$$

Factor 5624=2^{2}\times 1406. Rewrite the square root of the product \sqrt{2^{2}\times 1406} as the product of square roots \sqrt{2^{2}}\sqrt{1406}. Take the square root of 2^{2}.

$$\frac{2\sqrt{1406}}{\sqrt{625}}$$

Calculate the square root of 625 and get 25.

$$\frac{2\sqrt{1406}}{25}$$