Solve frac{24sqrt{18}}{9sqrt{32}}

$$\frac { 24 \sqrt { 18 } } { 9 \sqrt { 32 } }$$

Evaluate

$$2$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{8\sqrt{18}}{3\sqrt{32}}$$

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}.

$$\frac{8\times 3\sqrt{2}}{3\sqrt{32}}$$

Multiply 8 and 3 to get 24.

$$\frac{24\sqrt{2}}{3\sqrt{32}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{24\sqrt{2}}{3\times 4\sqrt{2}}$$

Multiply 3 and 4 to get 12.

$$\frac{24\sqrt{2}}{12\sqrt{2}}$$

Cancel out 12\sqrt{2} in both numerator and denominator.

$$2$$

Factor

$$2$$