Solve 50*10^8sqrt{1-(29.76*3.6/3*10^8)^2}

$$50 \times 10 ^ { 8 } \sqrt { 1 - ( \frac { 29.76 \times 3.6 } { 3 \times 10 ^ { 8 } } ) ^ { 2 } }$$

Evaluate

$$\frac{32\sqrt{610351562499922159}}{5}\approx 4999999999.999681473$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$50\times 100000000\sqrt{1-\left(\frac{29.76\times 3.6}{3\times 10^{8}}\right)^{2}}$$

Multiply 50 and 100000000 to get 5000000000.

$$5000000000\sqrt{1-\left(\frac{29.76\times 3.6}{3\times 10^{8}}\right)^{2}}$$

Multiply 29.76 and 3.6 to get 107.136.

$$5000000000\sqrt{1-\left(\frac{107.136}{3\times 10^{8}}\right)^{2}}$$

Calculate 10 to the power of 8 and get 100000000.

$$5000000000\sqrt{1-\left(\frac{107.136}{3\times 100000000}\right)^{2}}$$

Multiply 3 and 100000000 to get 300000000.

$$5000000000\sqrt{1-\left(\frac{107.136}{300000000}\right)^{2}}$$

Expand \frac{107.136}{300000000} by multiplying both numerator and the denominator by 1000.

$$5000000000\sqrt{1-\left(\frac{107136}{300000000000}\right)^{2}}$$

Reduce the fraction \frac{107136}{300000000000} to lowest terms by extracting and canceling out 384.

$$5000000000\sqrt{1-\left(\frac{279}{781250000}\right)^{2}}$$

Calculate \frac{279}{781250000} to the power of 2 and get \frac{77841}{610351562500000000}.

$$5000000000\sqrt{1-\frac{77841}{610351562500000000}}$$

Subtract \frac{77841}{610351562500000000} from 1 to get \frac{610351562499922159}{610351562500000000}.

$$5000000000\sqrt{\frac{610351562499922159}{610351562500000000}}$$

Rewrite the square root of the division \sqrt{\frac{610351562499922159}{610351562500000000}} as the division of square roots \frac{\sqrt{610351562499922159}}{\sqrt{610351562500000000}}.

$$5000000000\times \frac{\sqrt{610351562499922159}}{\sqrt{610351562500000000}}$$

Calculate the square root of 610351562500000000 and get 781250000.

$$5000000000\times \frac{\sqrt{610351562499922159}}{781250000}$$

Express 5000000000\times \frac{\sqrt{610351562499922159}}{781250000} as a single fraction.

$$\frac{5000000000\sqrt{610351562499922159}}{781250000}$$

Divide 5000000000\sqrt{610351562499922159} by 781250000 to get \frac{32}{5}\sqrt{610351562499922159}.

$$\frac{32}{5}\sqrt{610351562499922159}$$