Solve (4sqrt{6}-3sqrt{2})div2sqrt{2}

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

Evaluate

$$4\sqrt{3}-3\approx 3.92820323$$

Solution Steps

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

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

Use the distributive property to multiply 4\sqrt{6}-3\sqrt{2} by \sqrt{2}.

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

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{3}-3\left(\sqrt{2}\right)^{2}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{8\sqrt{3}-3\times 2}{2}$$

Multiply -3 and 2 to get -6.

$$\frac{8\sqrt{3}-6}{2}$$

Divide each term of 8\sqrt{3}-6 by 2 to get 4\sqrt{3}-3.

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