Solve 5^2/sqrt{16}-(3/2)^2+3^2/2:sqrt{1/4}=

$$\frac { 5 ^ { 2 } } { \sqrt { 16 } } - ( \frac { 3 } { 2 } ) ^ { 2 } + \frac { 3 ^ { 2 } } { 2 } : \sqrt { \frac { 1 } { 4 } } =$$

Evaluate

$$13$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{25}{\sqrt{16}}-\left(\frac{3}{2}\right)^{2}+\frac{\frac{3^{2}}{2}}{\sqrt{\frac{1}{4}}}$$

Calculate the square root of 16 and get 4.

$$\frac{25}{4}-\left(\frac{3}{2}\right)^{2}+\frac{\frac{3^{2}}{2}}{\sqrt{\frac{1}{4}}}$$

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

$$\frac{25}{4}-\frac{9}{4}+\frac{\frac{3^{2}}{2}}{\sqrt{\frac{1}{4}}}$$

Since \frac{25}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-9}{4}+\frac{\frac{3^{2}}{2}}{\sqrt{\frac{1}{4}}}$$

Subtract 9 from 25 to get 16.

$$\frac{16}{4}+\frac{\frac{3^{2}}{2}}{\sqrt{\frac{1}{4}}}$$

Divide 16 by 4 to get 4.

$$4+\frac{\frac{3^{2}}{2}}{\sqrt{\frac{1}{4}}}$$

Calculate 3 to the power of 2 and get 9.

$$4+\frac{\frac{9}{2}}{\sqrt{\frac{1}{4}}}$$

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.

$$4+\frac{\frac{9}{2}}{\frac{1}{2}}$$

Divide \frac{9}{2} by \frac{1}{2} by multiplying \frac{9}{2} by the reciprocal of \frac{1}{2}.

$$4+\frac{9}{2}\times 2$$

Cancel out 2 and 2.

$$4+9$$

Add 4 and 9 to get 13.

$$13$$

Factor

$$13$$