Solve frac{25*sqrt{20}}{160}

$$\frac{ 25 \times \sqrt{ 20 } }{ 160 }$$

Evaluate

$$\frac{5\sqrt{5}}{16}\approx 0.698771243$$

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}.

$$\frac{25\times 2\sqrt{5}}{160}$$

Multiply 25 and 2 to get 50.

$$\frac{50\sqrt{5}}{160}$$

Divide 50\sqrt{5} by 160 to get \frac{5}{16}\sqrt{5}.

$$\frac{5}{16}\sqrt{5}$$