Solve frac{15sqrt{2}*10^8}{frac{sqrt{3}}{10}}

$$\frac { 15 \sqrt { 2 } \times 10 ^ { 8 } } { \frac { \sqrt { 3 } } { 10 } }$$

Evaluate

$$5000000000\sqrt{6}\approx 12247448713.91588974$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\frac{15\sqrt{2}\times 100000000}{\frac{\sqrt{3}}{10}}$$

Multiply 15 and 100000000 to get 1500000000.

$$\frac{1500000000\sqrt{2}}{\frac{\sqrt{3}}{10}}$$

Divide 1500000000\sqrt{2} by \frac{\sqrt{3}}{10} by multiplying 1500000000\sqrt{2} by the reciprocal of \frac{\sqrt{3}}{10}.

$$\frac{1500000000\sqrt{2}\times 10}{\sqrt{3}}$$

Rationalize the denominator of \frac{1500000000\sqrt{2}\times 10}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{1500000000\sqrt{2}\times 10\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{1500000000\sqrt{2}\times 10\sqrt{3}}{3}$$

Multiply 1500000000 and 10 to get 15000000000.

$$\frac{15000000000\sqrt{2}\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{15000000000\sqrt{6}}{3}$$

Divide 15000000000\sqrt{6} by 3 to get 5000000000\sqrt{6}.

$$5000000000\sqrt{6}$$