Solve 70*sin45/5sqrt{6}=

$$\frac { 70 \cdot \sin 45 } { 5 \sqrt { 6 } } =$$

Evaluate

$$\frac{7\sqrt{3}}{3}\approx 4.041451884$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{14\sin(45)}{\sqrt{6}}$$

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

$$\frac{14\times \frac{\sqrt{2}}{2}}{\sqrt{6}}$$

Cancel out 2, the greatest common factor in 14 and 2.

$$\frac{7\sqrt{2}}{\sqrt{6}}$$

Rationalize the denominator of \frac{7\sqrt{2}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{7\sqrt{2}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{7\sqrt{2}\sqrt{6}}{6}$$

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}.

$$\frac{7\sqrt{2}\sqrt{2}\sqrt{3}}{6}$$

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

$$\frac{7\times 2\sqrt{3}}{6}$$

Multiply 7 and 2 to get 14.

$$\frac{14\sqrt{3}}{6}$$

Divide 14\sqrt{3} by 6 to get \frac{7}{3}\sqrt{3}.

$$\frac{7}{3}\sqrt{3}$$