Solve 3*sqrt{48/9}+frac{48sqrt{3}}{sqrt{48}}

$$3 \cdot \sqrt { \frac { 48 } { 9 } } + \frac { 48 \sqrt { 3 } } { \sqrt { 48 } }$$

Evaluate

$$4\sqrt{3}+12\approx 18.92820323$$

Solution Steps

Reduce the fraction \frac{48}{9} to lowest terms by extracting and canceling out 3.

$$3\sqrt{\frac{16}{3}}+\frac{48\sqrt{3}}{\sqrt{48}}$$

Rewrite the square root of the division \sqrt{\frac{16}{3}} as the division of square roots \frac{\sqrt{16}}{\sqrt{3}}.

$$3\times \frac{\sqrt{16}}{\sqrt{3}}+\frac{48\sqrt{3}}{\sqrt{48}}$$

Calculate the square root of 16 and get 4.

$$3\times \frac{4}{\sqrt{3}}+\frac{48\sqrt{3}}{\sqrt{48}}$$

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

$$3\times \frac{4\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\frac{48\sqrt{3}}{\sqrt{48}}$$

The square of \sqrt{3} is 3.

$$3\times \frac{4\sqrt{3}}{3}+\frac{48\sqrt{3}}{\sqrt{48}}$$

Cancel out 3 and 3.

$$4\sqrt{3}+\frac{48\sqrt{3}}{\sqrt{48}}$$

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}.

$$4\sqrt{3}+\frac{48\sqrt{3}}{4\sqrt{3}}$$

Cancel out 4\sqrt{3} in both numerator and denominator.

$$4\sqrt{3}+12$$

Factor

$$4 \sqrt{3} {(\sqrt{3} + 1)} = 18.92820323$$