Solve sqrt{108}*{left(cos(pi/12)right)}^2-sqrt{27}

$$\sqrt{ 108 } \times { \left( \cos ( \frac{ \pi }{ 12 } ) \right) }^{ 2 } - \sqrt{ 27 }$$

Evaluate

$$\frac{129903810567665804693817624619467\sqrt{3}}{50000000000000000000000000000000}\approx 4.5$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\sqrt{108} \cdot 0.9659258262890683 ^ {2} - \sqrt{27}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$6\sqrt{3}\times 0.9659258262890683^{2}-\sqrt{27}$$

Calculate 0.9659258262890683 to the power of 2 and get 0.93301270189221934897939208206489.

$$6\sqrt{3}\times 0.93301270189221934897939208206489-\sqrt{27}$$

Multiply 6 and 0.93301270189221934897939208206489 to get 5.59807621135331609387635249238934.

$$5.59807621135331609387635249238934\sqrt{3}-\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$5.59807621135331609387635249238934\sqrt{3}-3\sqrt{3}$$

Combine 5.59807621135331609387635249238934\sqrt{3} and -3\sqrt{3} to get 2.59807621135331609387635249238934\sqrt{3}.

$$2.59807621135331609387635249238934\sqrt{3}$$