Solve 9/16-sqrt{9/16}quad2.5+1

$$\frac { 9 } { 16 } - \sqrt { \frac { 9 } { 16 } } \quad 2.5 + 1$$

Evaluate

$$-0.3125$$

Solution Steps

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.

$$\frac{9}{16}-2.5\times \frac{3}{4}+1$$

Convert decimal number -2.5 to fraction -\frac{25}{10}. Reduce the fraction -\frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{9}{16}-\frac{5}{2}\times \frac{3}{4}+1$$

Multiply -\frac{5}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{16}+\frac{-5\times 3}{2\times 4}+1$$

Do the multiplications in the fraction \frac{-5\times 3}{2\times 4}.

$$\frac{9}{16}+\frac{-15}{8}+1$$

Fraction \frac{-15}{8} can be rewritten as -\frac{15}{8} by extracting the negative sign.

$$\frac{9}{16}-\frac{15}{8}+1$$

Least common multiple of 16 and 8 is 16. Convert \frac{9}{16} and \frac{15}{8} to fractions with denominator 16.

$$\frac{9}{16}-\frac{30}{16}+1$$

Since \frac{9}{16} and \frac{30}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-30}{16}+1$$

Subtract 30 from 9 to get -21.

$$-\frac{21}{16}+1$$

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

$$-\frac{21}{16}+\frac{16}{16}$$

Since -\frac{21}{16} and \frac{16}{16} have the same denominator, add them by adding their numerators.

$$\frac{-21+16}{16}$$

Add -21 and 16 to get -5.

$$-\frac{5}{16}$$

Factor

$$-0.3125$$