Solve 3sqrt{25/36}+sqrt{1/4}

$$3 \sqrt { \frac { 25 } { 36 } } + \sqrt { \frac { 1 } { 4 } }$$

Evaluate

$$3$$

Solution Steps

Rewrite the square root of the division \frac{25}{36} as the division of square roots \frac{\sqrt{25}}{\sqrt{36}}. Take the square root of both numerator and denominator.

$$3\times \frac{5}{6}+\sqrt{\frac{1}{4}}$$

Express 3\times \frac{5}{6} as a single fraction.

$$\frac{3\times 5}{6}+\sqrt{\frac{1}{4}}$$

Multiply 3 and 5 to get 15.

$$\frac{15}{6}+\sqrt{\frac{1}{4}}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{5}{2}+\sqrt{\frac{1}{4}}$$

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.

$$\frac{5}{2}+\frac{1}{2}$$

Since \frac{5}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{5+1}{2}$$

Add 5 and 1 to get 6.

$$\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$3$$

Factor

$$3$$