Solve frac{3sqrt{18}frac{sqrt{3}}{6}}{2}sqrt{86}

$$\frac{ 3 \sqrt{ 18 } \frac{ \sqrt{ 3 } }{ 6 } }{ 2 } \sqrt{ 86 }$$

Evaluate

$$\frac{3\sqrt{129}}{2}\approx 17.036725037$$

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}.

$$\frac{3\times 3\sqrt{2}\times \frac{\sqrt{3}}{6}}{2}\sqrt{86}$$

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{2}\times \frac{\sqrt{3}}{6}}{2}\sqrt{86}$$

Express 9\times \frac{\sqrt{3}}{6} as a single fraction.

$$\frac{\frac{9\sqrt{3}}{6}\sqrt{2}}{2}\sqrt{86}$$

Divide 9\sqrt{3} by 6 to get \frac{3}{2}\sqrt{3}.

$$\frac{\frac{3}{2}\sqrt{3}\sqrt{2}}{2}\sqrt{86}$$

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

$$\frac{\frac{3}{2}\sqrt{6}}{2}\sqrt{86}$$

Divide \frac{3}{2}\sqrt{6} by 2 to get \frac{3}{4}\sqrt{6}.

$$\frac{3}{4}\sqrt{6}\sqrt{86}$$

To multiply \sqrt{6} and \sqrt{86}, multiply the numbers under the square root.

$$\frac{3}{4}\sqrt{516}$$

Factor 516=2^{2}\times 129. Rewrite the square root of the product \sqrt{2^{2}\times 129} as the product of square roots \sqrt{2^{2}}\sqrt{129}. Take the square root of 2^{2}.

$$\frac{3}{4}\times 2\sqrt{129}$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{3\times 2}{4}\sqrt{129}$$

Multiply 3 and 2 to get 6.

$$\frac{6}{4}\sqrt{129}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}\sqrt{129}$$