Solve sqrt{27}*sqrt{1/3}+(1-sqrt{3})^0+|-2|-(1/2)

$$\sqrt { 27 } \times \sqrt { \frac { 1 } { 3 } } + ( 1 - \sqrt { 3 } ) ^ { 0 } + | - 2 | - ( \frac { 1 } { 2 } )$$

Evaluate

$$\frac{11}{2}=5.5$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

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

Calculate the square root of 1 and get 1.

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

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Cancel out 3 and 3.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Calculate 1-\sqrt{3} to the power of 0 and get 1.

$$3+1+|-2|-\frac{1}{2}$$

Add 3 and 1 to get 4.

$$4+|-2|-\frac{1}{2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

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

Add 4 and 2 to get 6.

$$6-\frac{1}{2}$$

Subtract \frac{1}{2} from 6 to get \frac{11}{2}.

$$\frac{11}{2}$$

Factor

$$\frac{11}{2} = 5\frac{1}{2} = 5.5$$