Solve (3sqrt{48}-4sqrt{2})div2sqrt{3})

$$( 3 \sqrt { 48 } - 4 \sqrt { 2 } ) \div 2 \sqrt { 3 } )$$

Evaluate

$$18-2\sqrt{6}\approx 13.101020514$$

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}.

$$\frac{3\times 4\sqrt{3}-4\sqrt{2}}{2}\sqrt{3}$$

Multiply 3 and 4 to get 12.

$$\frac{12\sqrt{3}-4\sqrt{2}}{2}\sqrt{3}$$

Express \frac{12\sqrt{3}-4\sqrt{2}}{2}\sqrt{3} as a single fraction.

$$\frac{\left(12\sqrt{3}-4\sqrt{2}\right)\sqrt{3}}{2}$$

Use the distributive property to multiply 12\sqrt{3}-4\sqrt{2} by \sqrt{3}.

$$\frac{12\left(\sqrt{3}\right)^{2}-4\sqrt{2}\sqrt{3}}{2}$$

The square of \sqrt{3} is 3.

$$\frac{12\times 3-4\sqrt{2}\sqrt{3}}{2}$$

Multiply 12 and 3 to get 36.

$$\frac{36-4\sqrt{2}\sqrt{3}}{2}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{36-4\sqrt{6}}{2}$$