Solve sqrt{(7/7)^2-(1/9)^2}

$$\sqrt { ( \frac { 7 } { 7 } ) ^ { 2 } - ( \frac { 1 } { 9 } ) ^ { 2 } }$$

Evaluate

$$\frac{4\sqrt{5}}{9}\approx 0.99380799$$

Solution Steps

Divide 7 by 7 to get 1.

$$\sqrt{1^{2}-\left(\frac{1}{9}\right)^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\sqrt{1-\left(\frac{1}{9}\right)^{2}}$$

Calculate \frac{1}{9} to the power of 2 and get \frac{1}{81}.

$$\sqrt{1-\frac{1}{81}}$$

Subtract \frac{1}{81} from 1 to get \frac{80}{81}.

$$\sqrt{\frac{80}{81}}$$

Rewrite the square root of the division \sqrt{\frac{80}{81}} as the division of square roots \frac{\sqrt{80}}{\sqrt{81}}.

$$\frac{\sqrt{80}}{\sqrt{81}}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{4\sqrt{5}}{\sqrt{81}}$$

Calculate the square root of 81 and get 9.

$$\frac{4\sqrt{5}}{9}$$