Solve -9+8/(sqrt{(9)^2+(-4)^2)(sqrt{(-1)^2+(-2)^2)}}

$$\frac { - 9 + 8 } { ( \sqrt { ( 9 ) ^ { 2 } + ( - 4 ) ^ { 2 } } ) ( \sqrt { ( - 1 ) ^ { 2 } + ( - 2 ) ^ { 2 } ) } }$$

Evaluate

$$-\frac{\sqrt{485}}{485}\approx -0.045407661$$

Solution Steps

Add -9 and 8 to get -1.

$$\frac{-1}{\sqrt{9^{2}+\left(-4\right)^{2}}\sqrt{\left(-1\right)^{2}+\left(-2\right)^{2}}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{-1}{\sqrt{81+\left(-4\right)^{2}}\sqrt{\left(-1\right)^{2}+\left(-2\right)^{2}}}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{-1}{\sqrt{81+16}\sqrt{\left(-1\right)^{2}+\left(-2\right)^{2}}}$$

Add 81 and 16 to get 97.

$$\frac{-1}{\sqrt{97}\sqrt{\left(-1\right)^{2}+\left(-2\right)^{2}}}$$

Calculate -1 to the power of 2 and get 1.

$$\frac{-1}{\sqrt{97}\sqrt{1+\left(-2\right)^{2}}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{-1}{\sqrt{97}\sqrt{1+4}}$$

Add 1 and 4 to get 5.

$$\frac{-1}{\sqrt{97}\sqrt{5}}$$

To multiply \sqrt{97} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{-1}{\sqrt{485}}$$

Rationalize the denominator of \frac{-1}{\sqrt{485}} by multiplying numerator and denominator by \sqrt{485}.

$$\frac{-\sqrt{485}}{\left(\sqrt{485}\right)^{2}}$$

The square of \sqrt{485} is 485.

$$\frac{-\sqrt{485}}{485}$$