Solve -1^2+sqrt{18}-4cos45^circ

$$- 1 ^ { 2 } + \sqrt { 18 } - 4 \cos 45 ^ { \circ }$$

Evaluate

$$\sqrt{2}-1\approx 0.414213562$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$-1+\sqrt{18}-4\cos(45)$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$-1+3\sqrt{2}-4\cos(45)$$

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

$$-1+3\sqrt{2}-4\times \frac{\sqrt{2}}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$-1+3\sqrt{2}-2\sqrt{2}$$

Combine 3\sqrt{2} and -2\sqrt{2} to get \sqrt{2}.

$$-1+\sqrt{2}$$