Solve sqrt{16div36+1div4}

$$\sqrt{ 16 \div 36+1 \div 4 }$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Reduce the fraction \frac{16}{36} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{4}{9}+\frac{1}{4}}$$

Least common multiple of 9 and 4 is 36. Convert \frac{4}{9} and \frac{1}{4} to fractions with denominator 36.

$$\sqrt{\frac{16}{36}+\frac{9}{36}}$$

Since \frac{16}{36} and \frac{9}{36} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{16+9}{36}}$$

Add 16 and 9 to get 25.

$$\sqrt{\frac{25}{36}}$$

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.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$