Solve 5sqrt{48}-7/2*sqrt{12}+frac{sqrt{75}}{3}-4sqrt{3}

$$5 \sqrt { 48 } - \frac { 7 } { 2 } \cdot \sqrt { 12 } + \frac { \sqrt { 75 } } { 3 } - 4 \sqrt { 3 }$$

Evaluate

$$\frac{32\sqrt{3}}{3}\approx 18.475208614$$

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}.

$$5\times 4\sqrt{3}-\frac{7}{2}\sqrt{12}+\frac{\sqrt{75}}{3}-4\sqrt{3}$$

Multiply 5 and 4 to get 20.

$$20\sqrt{3}-\frac{7}{2}\sqrt{12}+\frac{\sqrt{75}}{3}-4\sqrt{3}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$20\sqrt{3}-\frac{7}{2}\times 2\sqrt{3}+\frac{\sqrt{75}}{3}-4\sqrt{3}$$

Cancel out 2 and 2.

$$20\sqrt{3}-7\sqrt{3}+\frac{\sqrt{75}}{3}-4\sqrt{3}$$

Combine 20\sqrt{3} and -7\sqrt{3} to get 13\sqrt{3}.

$$13\sqrt{3}+\frac{\sqrt{75}}{3}-4\sqrt{3}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$13\sqrt{3}+\frac{5\sqrt{3}}{3}-4\sqrt{3}$$

Combine 13\sqrt{3} and \frac{5\sqrt{3}}{3} to get \frac{44}{3}\sqrt{3}.

$$\frac{44}{3}\sqrt{3}-4\sqrt{3}$$

Combine \frac{44}{3}\sqrt{3} and -4\sqrt{3} to get \frac{32}{3}\sqrt{3}.

$$\frac{32}{3}\sqrt{3}$$