Solve sqrt{3}(frac{sqrt{3}}{3}-4)

$$\sqrt { 3 } ( \frac { \sqrt { 3 } } { 3 } - 4 )$$

Evaluate

$$1-4\sqrt{3}\approx -5.92820323$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{3}{3}.

$$\sqrt{3}\left(\frac{\sqrt{3}}{3}-\frac{4\times 3}{3}\right)$$

Since \frac{\sqrt{3}}{3} and \frac{4\times 3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{3}\times \frac{\sqrt{3}-4\times 3}{3}$$

Do the multiplications in \sqrt{3}-4\times 3.

$$\sqrt{3}\times \frac{\sqrt{3}-12}{3}$$

Express \sqrt{3}\times \frac{\sqrt{3}-12}{3} as a single fraction.

$$\frac{\sqrt{3}\left(\sqrt{3}-12\right)}{3}$$

Use the distributive property to multiply \sqrt{3} by \sqrt{3}-12.

$$\frac{\left(\sqrt{3}\right)^{2}-12\sqrt{3}}{3}$$

The square of \sqrt{3} is 3.

$$\frac{3-12\sqrt{3}}{3}$$

Divide each term of 3-12\sqrt{3} by 3 to get 1-4\sqrt{3}.

$$1-4\sqrt{3}$$

Factor

$$1-4\sqrt{3}$$