Solve 17:(2/3)^-1+sqrt{18}-2sin45^circ+12sqrt{2}-31

$$17 : ( \frac { 2 } { 3 } ) ^ { - 1 } + \sqrt { 18 } - 2 \sin 45 ^ { \circ } + 12 \sqrt { 2 } - 31$$

Evaluate

$$14\sqrt{2}-\frac{59}{3}\approx 0.132323207$$

Solution Steps

Calculate \frac{2}{3} to the power of -1 and get \frac{3}{2}.

$$\frac{17}{\frac{3}{2}}+\sqrt{18}-2\sin(45)+12\sqrt{2}-31$$

Divide 17 by \frac{3}{2} by multiplying 17 by the reciprocal of \frac{3}{2}.

$$17\times \frac{2}{3}+\sqrt{18}-2\sin(45)+12\sqrt{2}-31$$

Multiply 17 and \frac{2}{3} to get \frac{34}{3}.

$$\frac{34}{3}+\sqrt{18}-2\sin(45)+12\sqrt{2}-31$$

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}.

$$\frac{34}{3}+3\sqrt{2}-2\sin(45)+12\sqrt{2}-31$$

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

$$\frac{34}{3}+3\sqrt{2}-2\times \frac{\sqrt{2}}{2}+12\sqrt{2}-31$$

Cancel out 2 and 2.

$$\frac{34}{3}+3\sqrt{2}-\sqrt{2}+12\sqrt{2}-31$$

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

$$\frac{34}{3}+2\sqrt{2}+12\sqrt{2}-31$$

Combine 2\sqrt{2} and 12\sqrt{2} to get 14\sqrt{2}.

$$\frac{34}{3}+14\sqrt{2}-31$$

Subtract 31 from \frac{34}{3} to get -\frac{59}{3}.

$$-\frac{59}{3}+14\sqrt{2}$$