Solve frac{1-sqrt{48}}{-3sqrt{3}}

$$\frac{ 1- \sqrt{ 48 } }{ -3 \sqrt{ 3 } }$$

Evaluate

$$-\frac{\sqrt{3}}{9}+\frac{4}{3}\approx 1.140883244$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

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

Rationalize the denominator of \frac{1-4\sqrt{3}}{-3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(1-4\sqrt{3}\right)\sqrt{3}}{-3\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(1-4\sqrt{3}\right)\sqrt{3}}{-3\times 3}$$

Multiply -3 and 3 to get -9.

$$\frac{\left(1-4\sqrt{3}\right)\sqrt{3}}{-9}$$

Use the distributive property to multiply 1-4\sqrt{3} by \sqrt{3}.

$$\frac{\sqrt{3}-4\left(\sqrt{3}\right)^{2}}{-9}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}-4\times 3}{-9}$$

Multiply -4 and 3 to get -12.

$$\frac{\sqrt{3}-12}{-9}$$

Multiply both numerator and denominator by -1.

$$\frac{-\sqrt{3}+12}{9}$$