Solve sqrt{1+9/16}+sqrt{3-3/4}

$$\sqrt{ 1+ \frac{ 9 }{ 16 } } + \sqrt{ 3- \frac{ 3 }{ 4 } }$$

Evaluate

$$\frac{11}{4}=2.75$$

Solution Steps

Convert 1 to fraction \frac{16}{16}.

$$\sqrt{\frac{16}{16}+\frac{9}{16}}+\sqrt{3-\frac{3}{4}}$$

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

$$\sqrt{\frac{16+9}{16}}+\sqrt{3-\frac{3}{4}}$$

Add 16 and 9 to get 25.

$$\sqrt{\frac{25}{16}}+\sqrt{3-\frac{3}{4}}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{5}{4}+\sqrt{3-\frac{3}{4}}$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{5}{4}+\sqrt{\frac{12}{4}-\frac{3}{4}}$$

Since \frac{12}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{4}+\sqrt{\frac{12-3}{4}}$$

Subtract 3 from 12 to get 9.

$$\frac{5}{4}+\sqrt{\frac{9}{4}}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{5}{4}+\frac{3}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{5}{4}+\frac{6}{4}$$

Since \frac{5}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{5+6}{4}$$

Add 5 and 6 to get 11.

$$\frac{11}{4}$$

Factor

$$\frac{11}{2 ^ {2}} = 2\frac{3}{4} = 2.75$$