Solve 8.2/sqrt{2.4^2+9+8.2^2}

$$\frac { 8.2 } { \sqrt { 2.4 ^ { 2 } + 9 + 8.2 ^ { 2 } } }$$

Evaluate

$$\frac{\sqrt{82}}{10}\approx 0.905538514$$

Solution Steps

Calculate 2.4 to the power of 2 and get 5.76.

$$\frac{8.2}{\sqrt{5.76+9+8.2^{2}}}$$

Add 5.76 and 9 to get 14.76.

$$\frac{8.2}{\sqrt{14.76+8.2^{2}}}$$

Calculate 8.2 to the power of 2 and get 67.24.

$$\frac{8.2}{\sqrt{14.76+67.24}}$$

Add 14.76 and 67.24 to get 82.

$$\frac{8.2}{\sqrt{82}}$$

Rationalize the denominator of \frac{8.2}{\sqrt{82}} by multiplying numerator and denominator by \sqrt{82}.

$$\frac{8.2\sqrt{82}}{\left(\sqrt{82}\right)^{2}}$$

The square of \sqrt{82} is 82.

$$\frac{8.2\sqrt{82}}{82}$$

Divide 8.2\sqrt{82} by 82 to get 0.1\sqrt{82}.

$$0.1\sqrt{82}$$