Solve sqrt{4/3*5.5*10^-9*6.67*10^-11*3.14}

$$\sqrt { \frac { 4 } { 3 } \times 5.5 \times 10 ^ { - 9 } \times 6.67 \times 10 ^ { - 11 } \times 3.14 }$$

Evaluate

$$\frac{\sqrt{3455727}}{1500000000000}\approx 1.23930572 \cdot 10^{-9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -9 and -11 to get -20.

$$\sqrt{\frac{4}{3}\times 5.5\times 10^{-20}\times 6.67\times 3.14}$$

Multiply \frac{4}{3} and 5.5 to get \frac{22}{3}.

$$\sqrt{\frac{22}{3}\times 10^{-20}\times 6.67\times 3.14}$$

Calculate 10 to the power of -20 and get \frac{1}{100000000000000000000}.

$$\sqrt{\frac{22}{3}\times \frac{1}{100000000000000000000}\times 6.67\times 3.14}$$

Multiply \frac{22}{3} and \frac{1}{100000000000000000000} to get \frac{11}{150000000000000000000}.

$$\sqrt{\frac{11}{150000000000000000000}\times 6.67\times 3.14}$$

Multiply \frac{11}{150000000000000000000} and 6.67 to get \frac{7337}{15000000000000000000000}.

$$\sqrt{\frac{7337}{15000000000000000000000}\times 3.14}$$

Multiply \frac{7337}{15000000000000000000000} and 3.14 to get \frac{1151909}{750000000000000000000000}.

$$\sqrt{\frac{1151909}{750000000000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1151909}{750000000000000000000000}} as the division of square roots \frac{\sqrt{1151909}}{\sqrt{750000000000000000000000}}.

$$\frac{\sqrt{1151909}}{\sqrt{750000000000000000000000}}$$

Factor 750000000000000000000000=500000000000^{2}\times 3. Rewrite the square root of the product \sqrt{500000000000^{2}\times 3} as the product of square roots \sqrt{500000000000^{2}}\sqrt{3}. Take the square root of 500000000000^{2}.

$$\frac{\sqrt{1151909}}{500000000000\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{1151909}}{500000000000\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{1151909}\sqrt{3}}{500000000000\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{1151909}\sqrt{3}}{500000000000\times 3}$$

To multiply \sqrt{1151909} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{3455727}}{500000000000\times 3}$$

Multiply 500000000000 and 3 to get 1500000000000.

$$\frac{\sqrt{3455727}}{1500000000000}$$