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

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

Verify

Solution Steps

Divide \sqrt{3} by \sqrt{3} to get 1.

$$\frac{4}{\sqrt{3}}=\frac{4}{\sqrt{3}}\times 1\text{ and }\frac{4}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{4\sqrt{3}}{3}$$

Divide \sqrt{3} by \sqrt{3} to get 1.

$$\frac{4}{\sqrt{3}}=\frac{4}{\sqrt{3}}\times 1\text{ and }\frac{4}{\sqrt{3}}\times 1=\frac{4\sqrt{3}}{3}$$

Rationalize the denominator of \frac{4}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4\sqrt{3}}{\left(\sqrt{3}\right)^{2}}=\frac{4}{\sqrt{3}}\times 1\text{ and }\frac{4}{\sqrt{3}}\times 1=\frac{4\sqrt{3}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{3}}{3}=\frac{4}{\sqrt{3}}\times 1\text{ and }\frac{4}{\sqrt{3}}\times 1=\frac{4\sqrt{3}}{3}$$

Rationalize the denominator of \frac{4}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4\sqrt{3}}{3}=\frac{4\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times 1\text{ and }\frac{4}{\sqrt{3}}\times 1=\frac{4\sqrt{3}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{3}}{3}=\frac{4\sqrt{3}}{3}\times 1\text{ and }\frac{4}{\sqrt{3}}\times 1=\frac{4\sqrt{3}}{3}$$

Express \frac{4\sqrt{3}}{3}\times 1 as a single fraction.

$$\frac{4\sqrt{3}}{3}=\frac{4\sqrt{3}}{3}\text{ and }\frac{4}{\sqrt{3}}\times 1=\frac{4\sqrt{3}}{3}$$

Rationalize the denominator of \frac{4}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{4\sqrt{3}}{3}=\frac{4\sqrt{3}}{3}\text{ and }\frac{4\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\times 1=\frac{4\sqrt{3}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{4\sqrt{3}}{3}=\frac{4\sqrt{3}}{3}\text{ and }\frac{4\sqrt{3}}{3}\times 1=\frac{4\sqrt{3}}{3}$$

Express \frac{4\sqrt{3}}{3}\times 1 as a single fraction.

$$\frac{4\sqrt{3}}{3}=\frac{4\sqrt{3}}{3}\text{ and }\frac{4\sqrt{3}}{3}=\frac{4\sqrt{3}}{3}$$

Subtract \frac{4\sqrt{3}}{3} from both sides.

$$\frac{4\sqrt{3}}{3}-\frac{4\sqrt{3}}{3}=0\text{ and }\frac{4\sqrt{3}}{3}=\frac{4\sqrt{3}}{3}$$

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

$$0=0\text{ and }\frac{4\sqrt{3}}{3}=\frac{4\sqrt{3}}{3}$$

Compare 0 and 0.

$$\text{true}\text{ and }\frac{4\sqrt{3}}{3}=\frac{4\sqrt{3}}{3}$$

Subtract \frac{4\sqrt{3}}{3} from both sides.

$$\text{true}\text{ and }\frac{4\sqrt{3}}{3}-\frac{4\sqrt{3}}{3}=0$$

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

$$\text{true}\text{ and }0=0$$

Compare 0 and 0.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$