Solve 3sqrt{48}+3/5sqrt{3}

$$3 \sqrt { 48 } + \frac { 3 } { 5 \sqrt { 3 } }$$

Evaluate

$$\frac{61\sqrt{3}}{5}\approx 21.131019852$$

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}.

$$3\times 4\sqrt{3}+\frac{3}{5\sqrt{3}}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{3}+\frac{3}{5\sqrt{3}}$$

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

$$12\sqrt{3}+\frac{3\sqrt{3}}{5\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$12\sqrt{3}+\frac{3\sqrt{3}}{5\times 3}$$

Cancel out 3 in both numerator and denominator.

$$12\sqrt{3}+\frac{\sqrt{3}}{5}$$

Combine 12\sqrt{3} and \frac{\sqrt{3}}{5} to get \frac{61}{5}\sqrt{3}.

$$\frac{61}{5}\sqrt{3}$$