Solve 1/2*frac{2sqrt{3}}{3}*frac{4sqrt{3}}{3}*frac{sqrt{3}}{2}=frac{2sqrt{3}}{3}

$$\frac { 1 } { 2 } \times \frac { 2 \sqrt { 3 } } { 3 } \times \frac { 4 \sqrt { 3 } } { 3 } \times \frac { \sqrt { 3 } } { 2 } = \frac { 2 \sqrt { 3 } } { 3 }$$

Verify

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$\frac{1}{2}\times 2\sqrt{3}\times \frac{4\sqrt{3}}{3}\sqrt{3}=2\times 2\sqrt{3}$$

Cancel out 2 and 2.

$$\sqrt{3}\times \frac{4\sqrt{3}}{3}\sqrt{3}=2\times 2\sqrt{3}$$

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

$$3\times \frac{4\sqrt{3}}{3}=2\times 2\sqrt{3}$$

Cancel out 3 and 3.

$$4\sqrt{3}=2\times 2\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{3}=4\sqrt{3}$$

Subtract 4\sqrt{3} from both sides.

$$4\sqrt{3}-4\sqrt{3}=0$$

Combine 4\sqrt{3} and -4\sqrt{3} to get 0.

$$0=0$$

Compare 0 and 0.

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