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

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

Evaluate

$$\frac{300\sqrt{599}}{599}\approx 12.257667697$$

Solution Steps

Calculate 299 to the power of 2 and get 89401.

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

Calculate 300 to the power of 2 and get 90000.

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

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

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

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

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

Subtract 89401 from 90000 to get 599.

$$\frac{1}{\sqrt{\frac{599}{90000}}}$$

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

$$\frac{1}{\frac{\sqrt{599}}{\sqrt{90000}}}$$

Calculate the square root of 90000 and get 300.

$$\frac{1}{\frac{\sqrt{599}}{300}}$$

Divide 1 by \frac{\sqrt{599}}{300} by multiplying 1 by the reciprocal of \frac{\sqrt{599}}{300}.

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

Rationalize the denominator of \frac{300}{\sqrt{599}} by multiplying numerator and denominator by \sqrt{599}.

$$\frac{300\sqrt{599}}{\left(\sqrt{599}\right)^{2}}$$

The square of \sqrt{599} is 599.

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