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

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

Evaluate

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

Solution Steps

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

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

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

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

Add 16 and 9 to get 25.

$$\sqrt{\frac{25}{16}}+\sqrt{1-\frac{3}{4}}$$

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.

$$\frac{5}{4}+\sqrt{1-\frac{3}{4}}$$

Convert 1 to fraction \frac{4}{4}.

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

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

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

Subtract 3 from 4 to get 1.

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

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.

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

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{1}{2} to fractions with denominator 4.

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

Since \frac{5}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

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

Add 5 and 2 to get 7.

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

Factor

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