Solve sqrt{1div2+1div4+1div8+1div16}

$$\sqrt{ 1 \div 2+1 \div 4+1 \div 8+1 \div 16 }$$

Evaluate

$$\frac{\sqrt{15}}{4}\approx 0.968245837$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\sqrt{\frac{2}{4}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{2+1}{4}+\frac{1}{8}+\frac{1}{16}}$$

Add 2 and 1 to get 3.

$$\sqrt{\frac{3}{4}+\frac{1}{8}+\frac{1}{16}}$$

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{1}{8} to fractions with denominator 8.

$$\sqrt{\frac{6}{8}+\frac{1}{8}+\frac{1}{16}}$$

Since \frac{6}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{6+1}{8}+\frac{1}{16}}$$

Add 6 and 1 to get 7.

$$\sqrt{\frac{7}{8}+\frac{1}{16}}$$

Least common multiple of 8 and 16 is 16. Convert \frac{7}{8} and \frac{1}{16} to fractions with denominator 16.

$$\sqrt{\frac{14}{16}+\frac{1}{16}}$$

Since \frac{14}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{14+1}{16}}$$

Add 14 and 1 to get 15.

$$\sqrt{\frac{15}{16}}$$

Rewrite the square root of the division \sqrt{\frac{15}{16}} as the division of square roots \frac{\sqrt{15}}{\sqrt{16}}.

$$\frac{\sqrt{15}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{15}}{4}$$