Solve sqrt{6}sin45

$$\sqrt { 6 } \sin 45$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Get the value of \sin(45) from trigonometric values table.

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

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

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

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}.

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

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

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

Cancel out 2 and 2.

$$\sqrt{3}$$