Solve frac{50sqrt{50}}{20}

$$\frac{ 50 \sqrt{ 50 } }{ 20 }$$

Evaluate

$$\frac{25\sqrt{2}}{2}\approx 17.67766953$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{50\times 5\sqrt{2}}{20}$$

Multiply 50 and 5 to get 250.

$$\frac{250\sqrt{2}}{20}$$

Divide 250\sqrt{2} by 20 to get \frac{25}{2}\sqrt{2}.

$$\frac{25}{2}\sqrt{2}$$