Solve frac{sqrt{3}+sqrt{48}}{sqrt{6}}

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

Evaluate

$$\frac{5\sqrt{2}}{2}\approx 3.535533906$$

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}.

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

Combine \sqrt{3} and 4\sqrt{3} to get 5\sqrt{3}.

$$\frac{5\sqrt{3}}{\sqrt{6}}$$

Rationalize the denominator of \frac{5\sqrt{3}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{5\sqrt{3}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{5\sqrt{3}\sqrt{6}}{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{5\sqrt{3}\sqrt{3}\sqrt{2}}{6}$$

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

$$\frac{5\times 3\sqrt{2}}{6}$$

Multiply 5 and 3 to get 15.

$$\frac{15\sqrt{2}}{6}$$

Divide 15\sqrt{2} by 6 to get \frac{5}{2}\sqrt{2}.

$$\frac{5}{2}\sqrt{2}$$