Solve frac{(6sqrt{14}-4sqrt{2})*(2sqrt{2})}{(2sqrt{2})*(2sqrt{2})}

$$\frac { ( 6 \sqrt { 14 } - 4 \sqrt { 2 } ) \cdot ( 2 \sqrt { 2 } ) } { ( 2 \sqrt { 2 } ) \cdot ( 2 \sqrt { 2 } ) }$$

Evaluate

$$3\sqrt{7}-2\approx 5.937253933$$

Solution Steps

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

$$\frac{\left(6\sqrt{14}-4\sqrt{2}\right)\times 2\sqrt{2}}{2\times 2\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{2}\left(-4\sqrt{2}+6\sqrt{14}\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{2}\left(-4\sqrt{2}+6\sqrt{14}\right)}{4}$$

Use the distributive property to multiply \sqrt{2} by -4\sqrt{2}+6\sqrt{14}.

$$\frac{-4\left(\sqrt{2}\right)^{2}+6\sqrt{2}\sqrt{14}}{4}$$

The square of \sqrt{2} is 2.

$$\frac{-4\times 2+6\sqrt{2}\sqrt{14}}{4}$$

Multiply -4 and 2 to get -8.

$$\frac{-8+6\sqrt{2}\sqrt{14}}{4}$$

Factor 14=2\times 7. Rewrite the square root of the product \sqrt{2\times 7} as the product of square roots \sqrt{2}\sqrt{7}.

$$\frac{-8+6\sqrt{2}\sqrt{2}\sqrt{7}}{4}$$

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

$$\frac{-8+6\times 2\sqrt{7}}{4}$$

Multiply 6 and 2 to get 12.

$$\frac{-8+12\sqrt{7}}{4}$$

Divide each term of -8+12\sqrt{7} by 4 to get -2+3\sqrt{7}.

$$-2+3\sqrt{7}$$

Factor

$$3 \sqrt{7} - 2 = 5.937253933$$