Solve (4sqrt{3}+8sqrt{6})div2sqrt{3}

$$( 4 \sqrt { 3 } + 8 \sqrt { 6 } ) \div 2 \sqrt { 3 }$$

Evaluate

$$12\sqrt{2}+6\approx 22.970562748$$

Solution Steps

Express \frac{4\sqrt{3}+8\sqrt{6}}{2}\sqrt{3} as a single fraction.

$$\frac{\left(4\sqrt{3}+8\sqrt{6}\right)\sqrt{3}}{2}$$

Use the distributive property to multiply 4\sqrt{3}+8\sqrt{6} by \sqrt{3}.

$$\frac{4\left(\sqrt{3}\right)^{2}+8\sqrt{6}\sqrt{3}}{2}$$

The square of \sqrt{3} is 3.

$$\frac{4\times 3+8\sqrt{6}\sqrt{3}}{2}$$

Multiply 4 and 3 to get 12.

$$\frac{12+8\sqrt{6}\sqrt{3}}{2}$$

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}.

$$\frac{12+8\sqrt{3}\sqrt{2}\sqrt{3}}{2}$$

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

$$\frac{12+8\times 3\sqrt{2}}{2}$$

Multiply 8 and 3 to get 24.

$$\frac{12+24\sqrt{2}}{2}$$

Factor

$$6 {(2 \sqrt{2} + 1)} = 22.970562748$$