Solve 2*sqrt{1/4}+sqrt{25/31}

$$2 \cdot \sqrt { \frac { 1 } { 4 } } + \sqrt { \frac { 25 } { 31 } }$$

Evaluate

$$\frac{5\sqrt{31}}{31}+1\approx 1.89802651$$

Short Solution Steps

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$2\times \frac{1}{2}+\sqrt{\frac{25}{31}}$$

Cancel out 2 and 2.

$$1+\sqrt{\frac{25}{31}}$$

Rewrite the square root of the division \sqrt{\frac{25}{31}} as the division of square roots \frac{\sqrt{25}}{\sqrt{31}}.

$$1+\frac{\sqrt{25}}{\sqrt{31}}$$

Calculate the square root of 25 and get 5.

$$1+\frac{5}{\sqrt{31}}$$

Rationalize the denominator of \frac{5}{\sqrt{31}} by multiplying numerator and denominator by \sqrt{31}.

$$1+\frac{5\sqrt{31}}{\left(\sqrt{31}\right)^{2}}$$

The square of \sqrt{31} is 31.

$$1+\frac{5\sqrt{31}}{31}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{31}{31}.

$$\frac{31}{31}+\frac{5\sqrt{31}}{31}$$

Since \frac{31}{31} and \frac{5\sqrt{31}}{31} have the same denominator, add them by adding their numerators.

$$\frac{31+5\sqrt{31}}{31}$$