Solve frac{sqrt{192}*sqrt{32}}{sqrt{24}}

$$\frac { \sqrt { 192 } \cdot \sqrt { 32 } } { \sqrt { 24 } }$$

Evaluate

$$16$$

Solution Steps

Factor 192=32\times 6. Rewrite the square root of the product \sqrt{32\times 6} as the product of square roots \sqrt{32}\sqrt{6}.

$$\frac{\sqrt{32}\sqrt{6}\sqrt{32}}{\sqrt{24}}$$

Multiply \sqrt{32} and \sqrt{32} to get 32.

$$\frac{32\sqrt{6}}{\sqrt{24}}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{32\sqrt{6}}{2\sqrt{6}}$$

Cancel out 2\sqrt{6} in both numerator and denominator.

$$16$$

Factor

$$2^{4}$$