Solve sqrt{32}-8sin45^circ-(1/4)^-1

$$\sqrt { 32 } - 8 \sin 45 ^ { \circ } - ( \frac { 1 } { 4 } ) ^ { - 1 }$$

Evaluate

$$-4$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$4\sqrt{2}-8\sin(45)-\left(\frac{1}{4}\right)^{-1}$$

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

$$4\sqrt{2}-8\times \frac{\sqrt{2}}{2}-\left(\frac{1}{4}\right)^{-1}$$

Cancel out 2, the greatest common factor in 8 and 2.

$$4\sqrt{2}-4\sqrt{2}-\left(\frac{1}{4}\right)^{-1}$$

Combine 4\sqrt{2} and -4\sqrt{2} to get 0.

$$0-\left(\frac{1}{4}\right)^{-1}$$

Calculate \frac{1}{4} to the power of -1 and get 4.

$$0-4$$

Subtract 4 from 0 to get -4.

$$-4$$