Solve sqrt{1-299^2div300^2}

$$\sqrt{ 1- { 299 }^{ 2 } \div { 300 }^{ 2 } }$$

Evaluate

$$\frac{\sqrt{599}}{300}\approx 0.081581588$$

Solution Steps

Calculate 299 to the power of 2 and get 89401.

$$\sqrt{1-\frac{89401}{300^{2}}}$$

Calculate 300 to the power of 2 and get 90000.

$$\sqrt{1-\frac{89401}{90000}}$$

Convert 1 to fraction \frac{90000}{90000}.

$$\sqrt{\frac{90000}{90000}-\frac{89401}{90000}}$$

Since \frac{90000}{90000} and \frac{89401}{90000} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{90000-89401}{90000}}$$

Subtract 89401 from 90000 to get 599.

$$\sqrt{\frac{599}{90000}}$$

Rewrite the square root of the division \sqrt{\frac{599}{90000}} as the division of square roots \frac{\sqrt{599}}{\sqrt{90000}}.

$$\frac{\sqrt{599}}{\sqrt{90000}}$$

Calculate the square root of 90000 and get 300.

$$\frac{\sqrt{599}}{300}$$