Solve -14:sqrt{18}-2sin45^circ+(pi-3)^0-(1/2)^-2

$$- 14 : \sqrt { 18 } - 2 \sin 45 ^ { \circ } + ( \pi - 3 ) ^ { 0 } - ( \frac { 1 } { 2 } ) ^ { - 2 }$$

Evaluate

$$-\frac{10\sqrt{2}}{3}-3\approx -7.714045208$$

Solution Steps

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}.

$$\frac{-14}{3\sqrt{2}}-2\sin(45)+\left(\pi -3\right)^{0}-\left(\frac{1}{2}\right)^{-2}$$

Rationalize the denominator of \frac{-14}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-14\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}-2\sin(45)+\left(\pi -3\right)^{0}-\left(\frac{1}{2}\right)^{-2}$$

The square of \sqrt{2} is 2.

$$\frac{-14\sqrt{2}}{3\times 2}-2\sin(45)+\left(\pi -3\right)^{0}-\left(\frac{1}{2}\right)^{-2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-7\sqrt{2}}{3}-2\sin(45)+\left(\pi -3\right)^{0}-\left(\frac{1}{2}\right)^{-2}$$

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

$$\frac{-7\sqrt{2}}{3}-2\times \frac{\sqrt{2}}{2}+\left(\pi -3\right)^{0}-\left(\frac{1}{2}\right)^{-2}$$

Cancel out 2 and 2.

$$\frac{-7\sqrt{2}}{3}-\sqrt{2}+\left(\pi -3\right)^{0}-\left(\frac{1}{2}\right)^{-2}$$

Combine \frac{-7\sqrt{2}}{3} and -\sqrt{2} to get -\frac{10}{3}\sqrt{2}.

$$-\frac{10}{3}\sqrt{2}+\left(\pi -3\right)^{0}-\left(\frac{1}{2}\right)^{-2}$$

Calculate \pi -3 to the power of 0 and get 1.

$$-\frac{10}{3}\sqrt{2}+1-\left(\frac{1}{2}\right)^{-2}$$

Calculate \frac{1}{2} to the power of -2 and get 4.

$$-\frac{10}{3}\sqrt{2}+1-4$$

Subtract 4 from 1 to get -3.

$$-\frac{10}{3}\sqrt{2}-3$$