Solve frac{3sqrt{162}}{sqrt{18}}

$$\frac { 3 \sqrt { 162 } } { \sqrt { 18 } }$$

Evaluate

$$9$$

Solution Steps

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$\frac{3\times 9\sqrt{2}}{\sqrt{18}}$$

Multiply 3 and 9 to get 27.

$$\frac{27\sqrt{2}}{\sqrt{18}}$$

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}.

$$\frac{27\sqrt{2}}{3\sqrt{2}}$$

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

$$9$$

Factor

$$3^{2}$$