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

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

Evaluate

$$\frac{3}{2}=1.5$$

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}.

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

Multiply 3 and 3 to get 9.

$$\frac{9\sqrt{2}}{\sqrt{72}}$$

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}.

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

Cancel out 3\sqrt{2} in both numerator and denominator.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$