Solve 13*20left(1-sqrt{1-1divleft(1*3right)^2}right)

$$13 \cdot 20 \left( 1- \sqrt{ 1-1 \div { \left(1 \cdot 3 \right) }^{ 2 } } \right)$$

Evaluate

$$-\frac{520\sqrt{2}}{3}+260\approx 14.869649189$$

Short Solution Steps

Multiply 13 and 20 to get 260.

$$260\left(1-\sqrt{1-\frac{1}{\left(1\times 3\right)^{2}}}\right)$$

Multiply 1 and 3 to get 3.

$$260\left(1-\sqrt{1-\frac{1}{3^{2}}}\right)$$

Calculate 3 to the power of 2 and get 9.

$$260\left(1-\sqrt{1-\frac{1}{9}}\right)$$

Subtract \frac{1}{9} from 1 to get \frac{8}{9}.

$$260\left(1-\sqrt{\frac{8}{9}}\right)$$

Rewrite the square root of the division \sqrt{\frac{8}{9}} as the division of square roots \frac{\sqrt{8}}{\sqrt{9}}.

$$260\left(1-\frac{\sqrt{8}}{\sqrt{9}}\right)$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$260\left(1-\frac{2\sqrt{2}}{\sqrt{9}}\right)$$

Calculate the square root of 9 and get 3.

$$260\left(1-\frac{2\sqrt{2}}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3}{3}.

$$260\left(\frac{3}{3}-\frac{2\sqrt{2}}{3}\right)$$

Since \frac{3}{3} and \frac{2\sqrt{2}}{3} have the same denominator, subtract them by subtracting their numerators.

$$260\times \frac{3-2\sqrt{2}}{3}$$

Express 260\times \frac{3-2\sqrt{2}}{3} as a single fraction.

$$\frac{260\left(3-2\sqrt{2}\right)}{3}$$

Use the distributive property to multiply 260 by 3-2\sqrt{2}.

$$\frac{780-520\sqrt{2}}{3}$$

Factor

$$\frac{260 {(3 - 2 \sqrt{2})}}{3} = 14.869649188663509$$