Solve sqrt{1-{left(1/1.005right)}^2}*3*1000

$$\sqrt{ 1- { \left( \frac{ 1 }{ 1.005 } \right) }^{ 2 } } \times 3 \times 1000$$

Evaluate

$$\frac{1000\sqrt{401}}{67}\approx 298.880364097$$

Solution Steps

Multiply 3 and 1000 to get 3000.

$$3000\sqrt{1-\left(\frac{1}{1.005}\right)^{2}}$$

Expand \frac{1}{1.005} by multiplying both numerator and the denominator by 1000.

$$3000\sqrt{1-\left(\frac{1000}{1005}\right)^{2}}$$

Reduce the fraction \frac{1000}{1005} to lowest terms by extracting and canceling out 5.

$$3000\sqrt{1-\left(\frac{200}{201}\right)^{2}}$$

Calculate \frac{200}{201} to the power of 2 and get \frac{40000}{40401}.

$$3000\sqrt{1-\frac{40000}{40401}}$$

Subtract \frac{40000}{40401} from 1 to get \frac{401}{40401}.

$$3000\sqrt{\frac{401}{40401}}$$

Rewrite the square root of the division \sqrt{\frac{401}{40401}} as the division of square roots \frac{\sqrt{401}}{\sqrt{40401}}.

$$3000\times \frac{\sqrt{401}}{\sqrt{40401}}$$

Calculate the square root of 40401 and get 201.

$$3000\times \frac{\sqrt{401}}{201}$$

Express 3000\times \frac{\sqrt{401}}{201} as a single fraction.

$$\frac{3000\sqrt{401}}{201}$$

Divide 3000\sqrt{401} by 201 to get \frac{1000}{67}\sqrt{401}.

$$\frac{1000}{67}\sqrt{401}$$