Solve 2(-3/sqrt{73})(-8/sqrt{73})

$$2 ( - \frac { 3 } { \sqrt { 73 } } ) ( - \frac { 8 } { \sqrt { 73 } } )$$

Evaluate

$$\frac{48}{73}\approx 0.657534247$$

Solution Steps

Rationalize the denominator of \frac{3}{\sqrt{73}} by multiplying numerator and denominator by \sqrt{73}.

$$2\left(-\frac{3\sqrt{73}}{\left(\sqrt{73}\right)^{2}}\right)\left(-\frac{8}{\sqrt{73}}\right)$$

The square of \sqrt{73} is 73.

$$2\left(-\frac{3\sqrt{73}}{73}\right)\left(-\frac{8}{\sqrt{73}}\right)$$

Rationalize the denominator of \frac{8}{\sqrt{73}} by multiplying numerator and denominator by \sqrt{73}.

$$2\left(-\frac{3\sqrt{73}}{73}\right)\left(-\frac{8\sqrt{73}}{\left(\sqrt{73}\right)^{2}}\right)$$

The square of \sqrt{73} is 73.

$$2\left(-\frac{3\sqrt{73}}{73}\right)\left(-\frac{8\sqrt{73}}{73}\right)$$

Express 2\left(-\frac{3\sqrt{73}}{73}\right) as a single fraction.

$$\frac{-2\times 3\sqrt{73}}{73}\left(-\frac{8\sqrt{73}}{73}\right)$$

Multiply \frac{-2\times 3\sqrt{73}}{73} times -\frac{8\sqrt{73}}{73} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-1\right)\times 2\times 3\sqrt{73}\times 8\sqrt{73}}{73\times 73}$$

Multiply \sqrt{73} and \sqrt{73} to get 73.

$$\frac{-\left(-1\right)\times 2\times 3\times 73\times 8}{73\times 73}$$

Cancel out 73 in both numerator and denominator.

$$\frac{-\left(-1\right)\times 2\times 3\times 8}{73}$$

Multiply -1 and -1 to get 1.

$$\frac{2\times 3\times 8}{73}$$

Multiply 2 and 3 to get 6.

$$\frac{6\times 8}{73}$$

Multiply 6 and 8 to get 48.

$$\frac{48}{73}$$

Factor

$$\frac{2 ^ {4} \cdot 3}{73} = 0.6575342465753424$$