Solve frac{frac{sqrt{72}}{3/2}sqrt{2}}{2}sqrt{18}

$$\frac{ \frac{ \sqrt{ 72 } }{ \frac{ 3 }{ 2 } } \sqrt{ 2 } }{ 2 } \sqrt{ 18 }$$

Evaluate

$$12\sqrt{2}\approx 16.970562748$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

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

Divide 6\sqrt{2} by \frac{3}{2} by multiplying 6\sqrt{2} by the reciprocal of \frac{3}{2}.

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

Multiply 6 and 2 to get 12.

$$\frac{\frac{12\sqrt{2}}{3}\sqrt{2}}{2}\sqrt{18}$$

Divide 12\sqrt{2} by 3 to get 4\sqrt{2}.

$$\frac{4\sqrt{2}\sqrt{2}}{2}\sqrt{18}$$

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

$$\frac{4\times 2}{2}\sqrt{18}$$

Multiply 4 and 2 to get 8.

$$\frac{8}{2}\sqrt{18}$$

Divide 8 by 2 to get 4.

$$4\sqrt{18}$$

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}.

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

Multiply 4 and 3 to get 12.

$$12\sqrt{2}$$