Solve 3sqrt{2}*frac{sqrt{10}}{2}div2sqrt{15}

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

Evaluate

$$\frac{15\sqrt{3}}{2}\approx 12.990381057$$

Solution Steps

Express 3\times \frac{\sqrt{10}}{2} as a single fraction.

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

Express \frac{3\sqrt{10}}{2}\sqrt{2} as a single fraction.

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

Express \frac{\frac{3\sqrt{10}\sqrt{2}}{2}}{2} as a single fraction.

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

Express \frac{3\sqrt{10}\sqrt{2}}{2\times 2}\sqrt{15} as a single fraction.

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

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$\frac{3\times 2\sqrt{5}\sqrt{5}\sqrt{3}}{2\times 2}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{3\times 2\times 5\sqrt{3}}{2\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{6\times 5\sqrt{3}}{2\times 2}$$

Multiply 6 and 5 to get 30.

$$\frac{30\sqrt{3}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{30\sqrt{3}}{4}$$

Divide 30\sqrt{3} by 4 to get \frac{15}{2}\sqrt{3}.

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