Solve frac{sqrt{72}sqrt{24}}{sqrt{48}}

$$\frac{ \sqrt{ 72 } \sqrt{ 24 } }{ \sqrt{ 48 } }$$

Evaluate

$$6$$

Solution Steps

Factor 72=24\times 3. Rewrite the square root of the product \sqrt{24\times 3} as the product of square roots \sqrt{24}\sqrt{3}.

$$\frac{\sqrt{24}\sqrt{3}\sqrt{24}}{\sqrt{48}}$$

Multiply \sqrt{24} and \sqrt{24} to get 24.

$$\frac{24\sqrt{3}}{\sqrt{48}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

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

Cancel out 4\sqrt{3} in both numerator and denominator.

$$6$$

Factor

$$2\times 3$$