Solve 2sqrt{1/3}*3sqrt{2}+sqrt{8}+sqrt{2}-1|-pi^0+(1/2)

$$2 \sqrt { \frac { 1 } { 3 } } \times 3 \sqrt { 2 } + \sqrt { 8 } + \sqrt { 2 } - 1 | - \pi ^ { 0 } + ( \frac { 1 } { 2 } )$$

Evaluate

$$2\sqrt{6}+3\sqrt{2}-\frac{1}{2}\approx 8.641620173$$

Solution Steps

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

$$2\times \frac{\sqrt{1}}{\sqrt{3}}\times 3\sqrt{2}+\sqrt{8}+\sqrt{2}-1|-\pi ^{0}+\frac{1}{2}|$$

Calculate the square root of 1 and get 1.

$$2\times \frac{1}{\sqrt{3}}\times 3\sqrt{2}+\sqrt{8}+\sqrt{2}-1|-\pi ^{0}+\frac{1}{2}|$$

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

$$2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times 3\sqrt{2}+\sqrt{8}+\sqrt{2}-1|-\pi ^{0}+\frac{1}{2}|$$

The square of \sqrt{3} is 3.

$$2\times \frac{\sqrt{3}}{3}\times 3\sqrt{2}+\sqrt{8}+\sqrt{2}-1|-\pi ^{0}+\frac{1}{2}|$$

Multiply 2 and 3 to get 6.

$$6\times \frac{\sqrt{3}}{3}\sqrt{2}+\sqrt{8}+\sqrt{2}-1|-\pi ^{0}+\frac{1}{2}|$$

Cancel out 3, the greatest common factor in 6 and 3.

$$2\sqrt{3}\sqrt{2}+\sqrt{8}+\sqrt{2}-1|-\pi ^{0}+\frac{1}{2}|$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{3}\sqrt{2}+2\sqrt{2}+\sqrt{2}-1|-\pi ^{0}+\frac{1}{2}|$$

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

$$2\sqrt{3}\sqrt{2}+3\sqrt{2}-1|-\pi ^{0}+\frac{1}{2}|$$

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

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

Add -1 and \frac{1}{2} to get -\frac{1}{2}.

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

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{2} is \frac{1}{2}.

$$2\sqrt{3}\sqrt{2}+3\sqrt{2}-1\times \frac{1}{2}$$

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

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$2\sqrt{6}+3\sqrt{2}-\frac{1}{2}$$