Solve sqrt{8}-1-4cos45^circ

$$\sqrt { 8 } - 1 - 4 \cos 45 ^ { \circ }$$

Evaluate

$$-1$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

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

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

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

Combine 2\sqrt{2} and -2\sqrt{2} to get 0.

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