Solve sqrt{1-1/1.465^2}

$$\sqrt{ 1- \frac{ 1 }{ { 1.465 }^{ 2 } } }$$

Evaluate

$$\frac{\sqrt{45849}}{293}\approx 0.730797938$$

Solution Steps

Calculate 1.465 to the power of 2 and get 2.146225.

$$\sqrt{1-\frac{1}{2.146225}}$$

Expand \frac{1}{2.146225} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{1-\frac{1000000}{2146225}}$$

Reduce the fraction \frac{1000000}{2146225} to lowest terms by extracting and canceling out 25.

$$\sqrt{1-\frac{40000}{85849}}$$

Convert 1 to fraction \frac{85849}{85849}.

$$\sqrt{\frac{85849}{85849}-\frac{40000}{85849}}$$

Since \frac{85849}{85849} and \frac{40000}{85849} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{85849-40000}{85849}}$$

Subtract 40000 from 85849 to get 45849.

$$\sqrt{\frac{45849}{85849}}$$

Rewrite the square root of the division \sqrt{\frac{45849}{85849}} as the division of square roots \frac{\sqrt{45849}}{\sqrt{85849}}.

$$\frac{\sqrt{45849}}{\sqrt{85849}}$$

Calculate the square root of 85849 and get 293.

$$\frac{\sqrt{45849}}{293}$$