Solve sqrt{5.19*10^9/6.67*10^-11*2.00*10^30}

$$\sqrt{ \frac{ 5.19 \times { 10 }^{ 9 } }{ 6.67 \times { 10 }^{ -11 } \times 2.00 \times { 10 }^{ 30 } } }$$

Evaluate

$$\frac{\sqrt{692346}}{133400000}\approx 0.000006237$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 30 to get 19.

$$\sqrt{\frac{5.19\times 10^{9}}{6.67\times 10^{19}\times 2}}$$

Cancel out 10^{9} in both numerator and denominator.

$$\sqrt{\frac{5.19}{2\times 6.67\times 10^{10}}}$$

Multiply 2 and 6.67 to get 13.34.

$$\sqrt{\frac{5.19}{13.34\times 10^{10}}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$\sqrt{\frac{5.19}{13.34\times 10000000000}}$$

Multiply 13.34 and 10000000000 to get 133400000000.

$$\sqrt{\frac{5.19}{133400000000}}$$

Expand \frac{5.19}{133400000000} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{519}{13340000000000}}$$

Rewrite the square root of the division \sqrt{\frac{519}{13340000000000}} as the division of square roots \frac{\sqrt{519}}{\sqrt{13340000000000}}.

$$\frac{\sqrt{519}}{\sqrt{13340000000000}}$$

Factor 13340000000000=100000^{2}\times 1334. Rewrite the square root of the product \sqrt{100000^{2}\times 1334} as the product of square roots \sqrt{100000^{2}}\sqrt{1334}. Take the square root of 100000^{2}.

$$\frac{\sqrt{519}}{100000\sqrt{1334}}$$

Rationalize the denominator of \frac{\sqrt{519}}{100000\sqrt{1334}} by multiplying numerator and denominator by \sqrt{1334}.

$$\frac{\sqrt{519}\sqrt{1334}}{100000\left(\sqrt{1334}\right)^{2}}$$

The square of \sqrt{1334} is 1334.

$$\frac{\sqrt{519}\sqrt{1334}}{100000\times 1334}$$

To multiply \sqrt{519} and \sqrt{1334}, multiply the numbers under the square root.

$$\frac{\sqrt{692346}}{100000\times 1334}$$

Multiply 100000 and 1334 to get 133400000.

$$\frac{\sqrt{692346}}{133400000}$$