Solve sqrt{15}*sqrt{12/3}

$$\sqrt { 15 } \times \sqrt { 1 \frac { 2 } { 3 } }$$

Evaluate

$$5$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\sqrt{15}\sqrt{\frac{3+2}{3}}$$

Add 3 and 2 to get 5.

$$\sqrt{15}\sqrt{\frac{5}{3}}$$

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

$$\sqrt{15}\times \frac{\sqrt{5}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\sqrt{15}\times \frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{15}\times \frac{\sqrt{5}\sqrt{3}}{3}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\sqrt{15}\times \frac{\sqrt{15}}{3}$$

Express \sqrt{15}\times \frac{\sqrt{15}}{3} as a single fraction.

$$\frac{\sqrt{15}\sqrt{15}}{3}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$\frac{15}{3}$$

Divide 15 by 3 to get 5.

$$5$$

Factor

$$5$$