Solve -4/3sqrt{18}div2sqrt{8}

$$- \frac { 4 } { 3 } \sqrt { 18 } \div 2 \sqrt { 8 }$$

Evaluate

$$-8$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Cancel out 3 and 3.

$$\frac{-4\sqrt{2}}{2}\sqrt{8}$$

Divide -4\sqrt{2} by 2 to get -2\sqrt{2}.

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

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$-2\sqrt{2}\times 2\sqrt{2}$$

Multiply -2 and 2 to get -4.

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

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

$$-4\times 2$$

Multiply -4 and 2 to get -8.

$$-8$$

Factor

$$-8$$