Solve 20000000divsqrt{80000000000/0.06}=

$$20000000 \div \sqrt{ \frac{ 80000000000 }{ 0.06 } } =$$

Evaluate

$$10\sqrt{3}\approx 17.320508076$$

Solution Steps

Expand \frac{80000000000}{0.06} by multiplying both numerator and the denominator by 100.

$$\frac{20000000}{\sqrt{\frac{8000000000000}{6}}}$$

Reduce the fraction \frac{8000000000000}{6} to lowest terms by extracting and canceling out 2.

$$\frac{20000000}{\sqrt{\frac{4000000000000}{3}}}$$

Rewrite the square root of the division \sqrt{\frac{4000000000000}{3}} as the division of square roots \frac{\sqrt{4000000000000}}{\sqrt{3}}.

$$\frac{20000000}{\frac{\sqrt{4000000000000}}{\sqrt{3}}}$$

Calculate the square root of 4000000000000 and get 2000000.

$$\frac{20000000}{\frac{2000000}{\sqrt{3}}}$$

Rationalize the denominator of \frac{2000000}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{20000000}{\frac{2000000\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}$$

The square of \sqrt{3} is 3.

$$\frac{20000000}{\frac{2000000\sqrt{3}}{3}}$$

Divide 20000000 by \frac{2000000\sqrt{3}}{3} by multiplying 20000000 by the reciprocal of \frac{2000000\sqrt{3}}{3}.

$$\frac{20000000\times 3}{2000000\sqrt{3}}$$

Cancel out 2000000 in both numerator and denominator.

$$\frac{3\times 10}{\sqrt{3}}$$

Rationalize the denominator of \frac{3\times 10}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{3\times 10\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{3\times 10\sqrt{3}}{3}$$

Multiply 3 and 10 to get 30.

$$\frac{30\sqrt{3}}{3}$$

Divide 30\sqrt{3} by 3 to get 10\sqrt{3}.

$$10\sqrt{3}$$