Solve sqrt{81/4}-sqrt{400}+sqrt{2.25}

$$\sqrt{ \frac{ 81 }{ 4 } } - \sqrt{ 400 } + \sqrt{ 2.25 }$$

Evaluate

$$-14$$

Solution Steps

Rewrite the square root of the division \frac{81}{4} as the division of square roots \frac{\sqrt{81}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{9}{2}-\sqrt{400}+\sqrt{2.25}$$

Calculate the square root of 400 and get 20.

$$\frac{9}{2}-20+\sqrt{2.25}$$

Convert 20 to fraction \frac{40}{2}.

$$\frac{9}{2}-\frac{40}{2}+\sqrt{2.25}$$

Since \frac{9}{2} and \frac{40}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-40}{2}+\sqrt{2.25}$$

Subtract 40 from 9 to get -31.

$$-\frac{31}{2}+\sqrt{2.25}$$

Calculate the square root of 2.25 and get 1.5.

$$-\frac{31}{2}+1.5$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{31}{2}+\frac{3}{2}$$

Since -\frac{31}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{-31+3}{2}$$

Add -31 and 3 to get -28.

$$\frac{-28}{2}$$

Divide -28 by 2 to get -14.

$$-14$$

Factor

$$-14$$