Solve sqrt{2*6.67*10^-11*7.34*10^22/1.74*10^6}

$$\sqrt { \frac { 2 \times 6.67 \times 10 ^ { - 11 } \times 7.34 \times 10 ^ { 22 } } { 1.74 \times 10 ^ { 6 } } }$$

Evaluate

$$\frac{20\sqrt{126615}}{3}\approx 2372.200103982$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 22 to get 11.

$$\sqrt{\frac{2\times 6.67\times 10^{11}\times 7.34}{1.74\times 10^{6}}}$$

Cancel out 10^{6} in both numerator and denominator.

$$\sqrt{\frac{2\times 6.67\times 7.34\times 10^{5}}{1.74}}$$

Multiply 2 and 6.67 to get 13.34.

$$\sqrt{\frac{13.34\times 7.34\times 10^{5}}{1.74}}$$

Multiply 13.34 and 7.34 to get 97.9156.

$$\sqrt{\frac{97.9156\times 10^{5}}{1.74}}$$

Calculate 10 to the power of 5 and get 100000.

$$\sqrt{\frac{97.9156\times 100000}{1.74}}$$

Multiply 97.9156 and 100000 to get 9791560.

$$\sqrt{\frac{9791560}{1.74}}$$

Expand \frac{9791560}{1.74} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{979156000}{174}}$$

Reduce the fraction \frac{979156000}{174} to lowest terms by extracting and canceling out 58.

$$\sqrt{\frac{16882000}{3}}$$

Rewrite the square root of the division \sqrt{\frac{16882000}{3}} as the division of square roots \frac{\sqrt{16882000}}{\sqrt{3}}.

$$\frac{\sqrt{16882000}}{\sqrt{3}}$$

Factor 16882000=20^{2}\times 42205. Rewrite the square root of the product \sqrt{20^{2}\times 42205} as the product of square roots \sqrt{20^{2}}\sqrt{42205}. Take the square root of 20^{2}.

$$\frac{20\sqrt{42205}}{\sqrt{3}}$$

Rationalize the denominator of \frac{20\sqrt{42205}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{20\sqrt{42205}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{20\sqrt{42205}\sqrt{3}}{3}$$

To multiply \sqrt{42205} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{20\sqrt{126615}}{3}$$