Solve sqrt{21/2+9/16}

$$\sqrt { 2 \frac { 1 } { 2 } + \frac { 9 } { 16 } }$$

Evaluate

$$\frac{7}{4}=1.75$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\sqrt{\frac{4+1}{2}+\frac{9}{16}}$$

Add 4 and 1 to get 5.

$$\sqrt{\frac{5}{2}+\frac{9}{16}}$$

Least common multiple of 2 and 16 is 16. Convert \frac{5}{2} and \frac{9}{16} to fractions with denominator 16.

$$\sqrt{\frac{40}{16}+\frac{9}{16}}$$

Since \frac{40}{16} and \frac{9}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{40+9}{16}}$$

Add 40 and 9 to get 49.

$$\sqrt{\frac{49}{16}}$$

Rewrite the square root of the division \frac{49}{16} as the division of square roots \frac{\sqrt{49}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{7}{4}$$

Factor

$$\frac{7}{2 ^ {2}} = 1\frac{3}{4} = 1.75$$