Solve -sqrt{36}+sqrt{21/4}+sqrt[3]{27}

$$- \sqrt { 36 } + \sqrt { 2 \frac { 1 } { 4 } } + \sqrt[ 3 ] { 27 }$$

Evaluate

$$-\frac{3}{2}=-1.5$$

Solution Steps

Calculate the square root of 36 and get 6.

$$-6+\sqrt{\frac{2\times 4+1}{4}}+\sqrt[3]{27}$$

Multiply 2 and 4 to get 8.

$$-6+\sqrt{\frac{8+1}{4}}+\sqrt[3]{27}$$

Add 8 and 1 to get 9.

$$-6+\sqrt{\frac{9}{4}}+\sqrt[3]{27}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$-6+\frac{3}{2}+\sqrt[3]{27}$$

Add -6 and \frac{3}{2} to get -\frac{9}{2}.

$$-\frac{9}{2}+\sqrt[3]{27}$$

Calculate \sqrt[3]{27} and get 3.

$$-\frac{9}{2}+3$$

Add -\frac{9}{2} and 3 to get -\frac{3}{2}.

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

Factor

$$-\frac{3}{2} = -1\frac{1}{2} = -1.5$$