Solve sqrt{25/98}

$$\sqrt { \frac { 25 } { 98 } }$$

Evaluate

$$\frac{5\sqrt{2}}{14}\approx 0.505076272$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{25}{98}} as the division of square roots \frac{\sqrt{25}}{\sqrt{98}}.

$$\frac{\sqrt{25}}{\sqrt{98}}$$

Calculate the square root of 25 and get 5.

$$\frac{5}{\sqrt{98}}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{5}{7\sqrt{2}}$$

Rationalize the denominator of \frac{5}{7\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{5\sqrt{2}}{7\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{5\sqrt{2}}{7\times 2}$$

Multiply 7 and 2 to get 14.

$$\frac{5\sqrt{2}}{14}$$