Solve 1/2sqrt{32}-3sqrt{1/2}-left(pi-3right)^0

$$\frac{ 1 }{ 2 } \sqrt{ 32 } -3 \sqrt{ \frac{ 1 }{ 2 } } - { \left( \pi -3 \right) }^{ 0 }$$

Evaluate

$$\frac{\sqrt{2}}{2}-1\approx -0.292893219$$

Short 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}.

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

Multiply \frac{1}{2} and 4 to get 2.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

Express -3\times \frac{\sqrt{2}}{2} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{2} times \frac{2}{2}.

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

Since \frac{2\times 2\sqrt{2}}{2} and \frac{-3\sqrt{2}}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\times 2\sqrt{2}-3\sqrt{2}.

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

Do the calculations in 4\sqrt{2}-3\sqrt{2}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

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

Since \frac{\sqrt{2}}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Factor

$$\frac{\sqrt{2} - 2}{2} = -0.2928932188134524$$