Solve sqrt{48}-6/sqrt{3}

$$\sqrt{ 48 } - \frac{ 6 }{ \sqrt{ 3 } }$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

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}.

$$4\sqrt{3}-\frac{6}{\sqrt{3}}$$

Rationalize the denominator of \frac{6}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$4\sqrt{3}-\frac{6\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$4\sqrt{3}-\frac{6\sqrt{3}}{3}$$

Divide 6\sqrt{3} by 3 to get 2\sqrt{3}.

$$4\sqrt{3}-2\sqrt{3}$$

Combine 4\sqrt{3} and -2\sqrt{3} to get 2\sqrt{3}.

$$2\sqrt{3}$$