Solve {c}{sqrt{18}+(pi+1)^0-4sqrt{1/2}}{-(-1/2)^-2}

$$\left. \begin{array} { c } { \sqrt { 18 } + ( \pi + 1 ) ^ { 0 } - 4 \sqrt { \frac { 1 } { 2 } } } \\ { - ( - \frac { 1 } { 2 } ) ^ { - 2 } } \end{array} \right.$$

Evaluate

$$\sqrt{2}-3\approx -1.585786438$$

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}.

$$3\sqrt{2}+\left(\pi +1\right)^{0}-4\sqrt{\frac{1}{2}}-\left(-\frac{1}{2}\right)^{-2}$$

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

$$3\sqrt{2}+1-4\sqrt{\frac{1}{2}}-\left(-\frac{1}{2}\right)^{-2}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$3\sqrt{2}+1-4\times \frac{\sqrt{1}}{\sqrt{2}}-\left(-\frac{1}{2}\right)^{-2}$$

Calculate the square root of 1 and get 1.

$$3\sqrt{2}+1-4\times \frac{1}{\sqrt{2}}-\left(-\frac{1}{2}\right)^{-2}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$3\sqrt{2}+1-4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\left(-\frac{1}{2}\right)^{-2}$$

The square of \sqrt{2} is 2.

$$3\sqrt{2}+1-4\times \frac{\sqrt{2}}{2}-\left(-\frac{1}{2}\right)^{-2}$$

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

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

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

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

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

$$\sqrt{2}+1-4$$

Subtract 4 from 1 to get -3.

$$\sqrt{2}-3$$