Solve 1sqrt{4/425}521

$$1 \sqrt{ \frac{ 4 }{ 425 } } 521$$

Evaluate

$$\frac{1042\sqrt{17}}{85}\approx 50.544424258$$

Solution Steps

Multiply 1 and 521 to get 521.

$$521\sqrt{\frac{4}{425}}$$

Rewrite the square root of the division \sqrt{\frac{4}{425}} as the division of square roots \frac{\sqrt{4}}{\sqrt{425}}.

$$521\times \frac{\sqrt{4}}{\sqrt{425}}$$

Calculate the square root of 4 and get 2.

$$521\times \frac{2}{\sqrt{425}}$$

Factor 425=5^{2}\times 17. Rewrite the square root of the product \sqrt{5^{2}\times 17} as the product of square roots \sqrt{5^{2}}\sqrt{17}. Take the square root of 5^{2}.

$$521\times \frac{2}{5\sqrt{17}}$$

Rationalize the denominator of \frac{2}{5\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$521\times \frac{2\sqrt{17}}{5\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$521\times \frac{2\sqrt{17}}{5\times 17}$$

Multiply 5 and 17 to get 85.

$$521\times \frac{2\sqrt{17}}{85}$$

Express 521\times \frac{2\sqrt{17}}{85} as a single fraction.

$$\frac{521\times 2\sqrt{17}}{85}$$

Multiply 521 and 2 to get 1042.

$$\frac{1042\sqrt{17}}{85}$$