Solve (4sqrt{2}-sqrt{6})divsqrt{2}=

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

Evaluate

$$4-\sqrt{3}\approx 2.267949192$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply 4 and 2 to get 8.

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

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}.

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

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

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

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

$$4-\sqrt{3}$$