Solve sqrt{1/4}+sqrt{9/16}+sqrt{25/16}=5/2

$$\sqrt { \frac { 1 } { 4 } } + \sqrt { \frac { 9 } { 16 } } + \sqrt { \frac { 25 } { 16 } } = \frac { 5 } { 2 }$$

Verify

Solution Steps

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.

$$\frac{1}{2}+\sqrt{\frac{9}{16}}+\sqrt{\frac{25}{16}}=\frac{5}{2}$$

Rewrite the square root of the division \frac{9}{16} as the division of square roots \frac{\sqrt{9}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{1}{2}+\frac{3}{4}+\sqrt{\frac{25}{16}}=\frac{5}{2}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{2}{4}+\frac{3}{4}+\sqrt{\frac{25}{16}}=\frac{5}{2}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{4}+\sqrt{\frac{25}{16}}=\frac{5}{2}$$

Add 2 and 3 to get 5.

$$\frac{5}{4}+\sqrt{\frac{25}{16}}=\frac{5}{2}$$

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.

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

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

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

Add 5 and 5 to get 10.

$$\frac{10}{4}=\frac{5}{2}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}=\frac{5}{2}$$

Compare \frac{5}{2} and \frac{5}{2}.

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