Solve frac{4sqrt{6}-6sqrt{2}}{2sqrt{2}}

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

Evaluate

$$2\sqrt{3}-3\approx 0.464101615$$

Solution Steps

Rationalize the denominator of \frac{4\sqrt{6}-6\sqrt{2}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

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

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

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

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}.

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

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

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

Multiply 4 and 2 to get 8.

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

The square of \sqrt{2} is 2.

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

Multiply -6 and 2 to get -12.

$$\frac{8\sqrt{3}-12}{4}$$

Divide each term of 8\sqrt{3}-12 by 4 to get 2\sqrt{3}-3.

$$2\sqrt{3}-3$$

Factor

$$2 \sqrt{3} - 3 = 0.464101615$$