Solve frac{sqrt{2}}{2}*5sqrt{6}

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

Evaluate

$$5\sqrt{3}\approx 8.660254038$$

Solution Steps

Express 5\times \frac{\sqrt{2}}{2} as a single fraction.

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

Express \frac{5\sqrt{2}}{2}\sqrt{6} as a single fraction.

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

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

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

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

Multiply 5 and 2 to get 10.

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

Divide 10\sqrt{3} by 2 to get 5\sqrt{3}.

$$5\sqrt{3}$$