Solve frac{sqrt{500}}{sqrt{10}*sqrt{32}}

$$\frac{ \sqrt{ 500 } }{ \sqrt{ 10 } \times \sqrt{ 32 } }$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$\frac{10\sqrt{5}}{\sqrt{10}\sqrt{32}}$$

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}.

$$\frac{10\sqrt{5}}{\sqrt{10}\times 4\sqrt{2}}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$\frac{10\sqrt{5}}{\sqrt{2}\sqrt{5}\times 4\sqrt{2}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{10\sqrt{5}}{2\times 4\sqrt{5}}$$

Cancel out 2\sqrt{5} in both numerator and denominator.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$