Solve 2sqrt{20}*1/4div4sqrt{5}

$$2 \sqrt { 20 } \times \frac { 1 } { 4 } \div 4 \sqrt { 5 }$$

Evaluate

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

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{2\times 2\sqrt{5}\times \frac{1}{4}}{4}\sqrt{5}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{5}\times \frac{1}{4}}{4}\sqrt{5}$$

Cancel out 4 and 4.

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

Express \frac{\sqrt{5}}{4}\sqrt{5} as a single fraction.

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

Factor

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