Solve 1/(-061)(001)(sqrt{2(3864)})(-2/5(4)^5/2)

$$\frac { 1 } { ( - 061 ) ( 001 ) ( \sqrt { 2 ( 3864 } ) } ) ( - \frac { 2 } { 5 } ( 4 ) ^ { 5 / 2 } )$$

Evaluate

$$\frac{16\sqrt{483}}{147315}\approx 0.002386968$$

Solution Steps

Multiply -61 and 1 to get -61.

$$\frac{1}{-61\sqrt{2\times 3864}}\left(-\frac{2}{5}\right)\times 4^{\frac{5}{2}}$$

Multiply 2 and 3864 to get 7728.

$$\frac{1}{-61\sqrt{7728}}\left(-\frac{2}{5}\right)\times 4^{\frac{5}{2}}$$

Factor 7728=4^{2}\times 483. Rewrite the square root of the product \sqrt{4^{2}\times 483} as the product of square roots \sqrt{4^{2}}\sqrt{483}. Take the square root of 4^{2}.

$$\frac{1}{-61\times 4\sqrt{483}}\left(-\frac{2}{5}\right)\times 4^{\frac{5}{2}}$$

Multiply -61 and 4 to get -244.

$$\frac{1}{-244\sqrt{483}}\left(-\frac{2}{5}\right)\times 4^{\frac{5}{2}}$$

Rationalize the denominator of \frac{1}{-244\sqrt{483}} by multiplying numerator and denominator by \sqrt{483}.

$$\frac{\sqrt{483}}{-244\left(\sqrt{483}\right)^{2}}\left(-\frac{2}{5}\right)\times 4^{\frac{5}{2}}$$

The square of \sqrt{483} is 483.

$$\frac{\sqrt{483}}{-244\times 483}\left(-\frac{2}{5}\right)\times 4^{\frac{5}{2}}$$

Multiply -244 and 483 to get -117852.

$$\frac{\sqrt{483}}{-117852}\left(-\frac{2}{5}\right)\times 4^{\frac{5}{2}}$$

Calculate 4 to the power of \frac{5}{2} and get 32.

$$\frac{\sqrt{483}}{-117852}\left(-\frac{2}{5}\right)\times 32$$

Multiply -\frac{2}{5} and 32 to get -\frac{64}{5}.

$$\frac{\sqrt{483}}{-117852}\left(-\frac{64}{5}\right)$$

Multiply \frac{\sqrt{483}}{-117852} times -\frac{64}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{483}\times 64}{-117852\times 5}$$

Cancel out 4 in both numerator and denominator.

$$\frac{-16\sqrt{483}}{-29463\times 5}$$

Multiply -29463 and 5 to get -147315.

$$\frac{-16\sqrt{483}}{-147315}$$