Solve 240/sqrt{240^2+120}

$$\frac { 240 } { \sqrt { 240 ^ { 2 } + 120 } }$$

Evaluate

$$\frac{4\sqrt{14430}}{481}\approx 0.998959958$$

Solution Steps

Calculate 240 to the power of 2 and get 57600.

$$\frac{240}{\sqrt{57600+120}}$$

Add 57600 and 120 to get 57720.

$$\frac{240}{\sqrt{57720}}$$

Factor 57720=2^{2}\times 14430. Rewrite the square root of the product \sqrt{2^{2}\times 14430} as the product of square roots \sqrt{2^{2}}\sqrt{14430}. Take the square root of 2^{2}.

$$\frac{240}{2\sqrt{14430}}$$

Rationalize the denominator of \frac{240}{2\sqrt{14430}} by multiplying numerator and denominator by \sqrt{14430}.

$$\frac{240\sqrt{14430}}{2\left(\sqrt{14430}\right)^{2}}$$

The square of \sqrt{14430} is 14430.

$$\frac{240\sqrt{14430}}{2\times 14430}$$

Cancel out 2\times 30 in both numerator and denominator.

$$\frac{4\sqrt{14430}}{481}$$