Solve cos(105^circ)*2*sqrt{52}

$$\cos ( 105 ^ { \circ } ) \times 2 \times \sqrt{ 52 }$$

Evaluate

$$-\frac{5176380902050417\sqrt{13}}{5000000000000000}\approx -3.732741353$$

Solution Steps

Evaluate trigonometric functions in the problem

$$-0.25881904510252085 \cdot 2 \cdot \sqrt{52}$$

Multiply 2 and -0.25881904510252085 to get -0.5176380902050417.

$$-0.5176380902050417\sqrt{52}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$-0.5176380902050417\times 2\sqrt{13}$$

Multiply -0.5176380902050417 and 2 to get -1.0352761804100834.

$$-1.0352761804100834\sqrt{13}$$