Solve sqrt{2*1,60*10^-19*6,00*10^4/9,17*10^-31*3,00}

$$\sqrt { \frac { 2 \times 1,60 \times 10 ^ { - 19 } \times 6,00 \times 10 ^ { 4 } } { 9,17 \times 10 ^ { - 31 } } \times 3,00 }$$

Evaluate

$$\frac{2400000000\sqrt{9170}}{917}\approx 250626260.307069749$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -19 and 4 to get -15.

$$\sqrt{\frac{2\times 1,6\times 10^{-15}\times 6}{9,17\times 10^{-31}}\times 3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\sqrt{\frac{1,6\times 2\times 6\times 10^{16}}{9,17}\times 3}$$

Multiply 1,6 and 2 to get 3,2.

$$\sqrt{\frac{3,2\times 6\times 10^{16}}{9,17}\times 3}$$

Multiply 3,2 and 6 to get 19,2.

$$\sqrt{\frac{19,2\times 10^{16}}{9,17}\times 3}$$

Calculate 10 to the power of 16 and get 10000000000000000.

$$\sqrt{\frac{19,2\times 10000000000000000}{9,17}\times 3}$$

Multiply 19,2 and 10000000000000000 to get 192000000000000000.

$$\sqrt{\frac{192000000000000000}{9,17}\times 3}$$

Expand \frac{192000000000000000}{9,17} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{19200000000000000000}{917}\times 3}$$

Multiply \frac{19200000000000000000}{917} and 3 to get \frac{57600000000000000000}{917}.

$$\sqrt{\frac{57600000000000000000}{917}}$$

Rewrite the square root of the division \sqrt{\frac{57600000000000000000}{917}} as the division of square roots \frac{\sqrt{57600000000000000000}}{\sqrt{917}}.

$$\frac{\sqrt{57600000000000000000}}{\sqrt{917}}$$

Factor 57600000000000000000=2400000000^{2}\times 10. Rewrite the square root of the product \sqrt{2400000000^{2}\times 10} as the product of square roots \sqrt{2400000000^{2}}\sqrt{10}. Take the square root of 2400000000^{2}.

$$\frac{2400000000\sqrt{10}}{\sqrt{917}}$$

Rationalize the denominator of \frac{2400000000\sqrt{10}}{\sqrt{917}} by multiplying numerator and denominator by \sqrt{917}.

$$\frac{2400000000\sqrt{10}\sqrt{917}}{\left(\sqrt{917}\right)^{2}}$$

The square of \sqrt{917} is 917.

$$\frac{2400000000\sqrt{10}\sqrt{917}}{917}$$

To multiply \sqrt{10} and \sqrt{917}, multiply the numbers under the square root.

$$\frac{2400000000\sqrt{9170}}{917}$$