Solve 4/3sqrt{18}div8sqrt{3}

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

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

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}.

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

Cancel out 3 and 3.

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

Divide 4\sqrt{2} by 8 to get \frac{1}{2}\sqrt{2}.

$$\frac{1}{2}\sqrt{2}\sqrt{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{1}{2}\sqrt{6}$$