Solve sqrt{25/4}-{left(3/2right)}^2=

$$\sqrt{ \frac{ 25 }{ 4 } } - { \left( \frac{ 3 }{ 2 } \right) }^{ 2 } =$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{5}{2}-\left(\frac{3}{2}\right)^{2}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{5}{2}-\frac{9}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{9}{4} to fractions with denominator 4.

$$\frac{10}{4}-\frac{9}{4}$$

Since \frac{10}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-9}{4}$$

Subtract 9 from 10 to get 1.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$