Solve sqrt{5/4}-sqrt{144}+sqrt{81}

$$\sqrt{ \frac{ 5 }{ 4 } } - \sqrt{ 144 } + \sqrt{ 81 }$$

Evaluate

$$\frac{\sqrt{5}}{2}-3\approx -1.881966011$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{4}} as the division of square roots \frac{\sqrt{5}}{\sqrt{4}}.

$$\frac{\sqrt{5}}{\sqrt{4}}-\sqrt{144}+\sqrt{81}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{5}}{2}-\sqrt{144}+\sqrt{81}$$

Calculate the square root of 144 and get 12.

$$\frac{\sqrt{5}}{2}-12+\sqrt{81}$$

Calculate the square root of 81 and get 9.

$$\frac{\sqrt{5}}{2}-12+9$$

Add -12 and 9 to get -3.

$$\frac{\sqrt{5}}{2}-3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\frac{\sqrt{5}}{2}-\frac{3\times 2}{2}$$

Since \frac{\sqrt{5}}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{5}-3\times 2}{2}$$

Do the multiplications in \sqrt{5}-3\times 2.

$$\frac{\sqrt{5}-6}{2}$$