Solve 2(sqrt{2*25*10^7})(sqrt{1493*10^-9})

$$2 ( \sqrt { 2 \cdot 25 \times 10 ^ { 7 } } ) ( \sqrt { 1493 \times 10 ^ { - 9 } } )$$

Evaluate

$$\sqrt{2986}\approx 54.644304369$$

Solution Steps

Multiply 2 and 25 to get 50.

$$2\sqrt{50\times 10^{7}}\sqrt{1493\times 10^{-9}}$$

Calculate 10 to the power of 7 and get 10000000.

$$2\sqrt{50\times 10000000}\sqrt{1493\times 10^{-9}}$$

Multiply 50 and 10000000 to get 500000000.

$$2\sqrt{500000000}\sqrt{1493\times 10^{-9}}$$

Factor 500000000=10000^{2}\times 5. Rewrite the square root of the product \sqrt{10000^{2}\times 5} as the product of square roots \sqrt{10000^{2}}\sqrt{5}. Take the square root of 10000^{2}.

$$2\times 10000\sqrt{5}\sqrt{1493\times 10^{-9}}$$

Multiply 2 and 10000 to get 20000.

$$20000\sqrt{5}\sqrt{1493\times 10^{-9}}$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$20000\sqrt{5}\sqrt{1493\times \frac{1}{1000000000}}$$

Multiply 1493 and \frac{1}{1000000000} to get \frac{1493}{1000000000}.

$$20000\sqrt{5}\sqrt{\frac{1493}{1000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1493}{1000000000}} as the division of square roots \frac{\sqrt{1493}}{\sqrt{1000000000}}.

$$20000\sqrt{5}\times \frac{\sqrt{1493}}{\sqrt{1000000000}}$$

Factor 1000000000=10000^{2}\times 10. Rewrite the square root of the product \sqrt{10000^{2}\times 10} as the product of square roots \sqrt{10000^{2}}\sqrt{10}. Take the square root of 10000^{2}.

$$20000\sqrt{5}\times \frac{\sqrt{1493}}{10000\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{1493}}{10000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$20000\sqrt{5}\times \frac{\sqrt{1493}\sqrt{10}}{10000\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$20000\sqrt{5}\times \frac{\sqrt{1493}\sqrt{10}}{10000\times 10}$$

To multiply \sqrt{1493} and \sqrt{10}, multiply the numbers under the square root.

$$20000\sqrt{5}\times \frac{\sqrt{14930}}{10000\times 10}$$

Multiply 10000 and 10 to get 100000.

$$20000\sqrt{5}\times \frac{\sqrt{14930}}{100000}$$

Cancel out 100000, the greatest common factor in 20000 and 100000.

$$\frac{\sqrt{14930}}{5}\sqrt{5}$$

Express \frac{\sqrt{14930}}{5}\sqrt{5} as a single fraction.

$$\frac{\sqrt{14930}\sqrt{5}}{5}$$

Factor 14930=5\times 2986. Rewrite the square root of the product \sqrt{5\times 2986} as the product of square roots \sqrt{5}\sqrt{2986}.

$$\frac{\sqrt{5}\sqrt{2986}\sqrt{5}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{5\sqrt{2986}}{5}$$

Cancel out 5 and 5.

$$\sqrt{2986}$$