Solve sqrt{599^2/33}*sin60^circ

$$\sqrt { \frac { 599 ^ { 2 } } { 33 } } \times \sin 60 ^ { \circ }$$

Evaluate

$$\frac{599\sqrt{11}}{22}\approx 90.302647701$$

Solution Steps

Calculate 599 to the power of 2 and get 358801.

$$\sqrt{\frac{358801}{33}}\sin(60)$$

Rewrite the square root of the division \sqrt{\frac{358801}{33}} as the division of square roots \frac{\sqrt{358801}}{\sqrt{33}}.

$$\frac{\sqrt{358801}}{\sqrt{33}}\sin(60)$$

Calculate the square root of 358801 and get 599.

$$\frac{599}{\sqrt{33}}\sin(60)$$

Rationalize the denominator of \frac{599}{\sqrt{33}} by multiplying numerator and denominator by \sqrt{33}.

$$\frac{599\sqrt{33}}{\left(\sqrt{33}\right)^{2}}\sin(60)$$

The square of \sqrt{33} is 33.

$$\frac{599\sqrt{33}}{33}\sin(60)$$

Get the value of \sin(60) from trigonometric values table.

$$\frac{599\sqrt{33}}{33}\times \frac{\sqrt{3}}{2}$$

Multiply \frac{599\sqrt{33}}{33} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{599\sqrt{33}\sqrt{3}}{33\times 2}$$

Factor 33=3\times 11. Rewrite the square root of the product \sqrt{3\times 11} as the product of square roots \sqrt{3}\sqrt{11}.

$$\frac{599\sqrt{3}\sqrt{11}\sqrt{3}}{33\times 2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{599\times 3\sqrt{11}}{33\times 2}$$

Multiply 599 and 3 to get 1797.

$$\frac{1797\sqrt{11}}{33\times 2}$$

Multiply 33 and 2 to get 66.

$$\frac{1797\sqrt{11}}{66}$$

Divide 1797\sqrt{11} by 66 to get \frac{599}{22}\sqrt{11}.

$$\frac{599}{22}\sqrt{11}$$