Solve 4sqrt{2}*3sqrt{15}divfrac{sqrt{2}}{sqrt{5}}

$$4 \sqrt { 2 } \times 3 \sqrt { 15 } \div \frac { \sqrt { 2 } } { \sqrt { 5 } }$$

Evaluate

$$60\sqrt{3}\approx 103.923048454$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{12\sqrt{2}\sqrt{15}}{\frac{\sqrt{2}}{\sqrt{5}}}$$

To multiply \sqrt{2} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{12\sqrt{30}}{\frac{\sqrt{2}}{\sqrt{5}}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{12\sqrt{30}}{\frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{12\sqrt{30}}{\frac{\sqrt{2}\sqrt{5}}{5}}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{12\sqrt{30}}{\frac{\sqrt{10}}{5}}$$

Divide 12\sqrt{30} by \frac{\sqrt{10}}{5} by multiplying 12\sqrt{30} by the reciprocal of \frac{\sqrt{10}}{5}.

$$\frac{12\sqrt{30}\times 5}{\sqrt{10}}$$

Rationalize the denominator of \frac{12\sqrt{30}\times 5}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{12\sqrt{30}\times 5\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{12\sqrt{30}\times 5\sqrt{10}}{10}$$

Multiply 12 and 5 to get 60.

$$\frac{60\sqrt{30}\sqrt{10}}{10}$$

Factor 30=10\times 3. Rewrite the square root of the product \sqrt{10\times 3} as the product of square roots \sqrt{10}\sqrt{3}.

$$\frac{60\sqrt{10}\sqrt{3}\sqrt{10}}{10}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$\frac{60\times 10\sqrt{3}}{10}$$

Cancel out 10 and 10.

$$60\sqrt{3}$$