Solve sqrt{(-3)^2}+sqrt{21/4}-sqrt[3]{-27}

$$\sqrt { ( - 3 ) ^ { 2 } } + \sqrt { 2 \frac { 1 } { 4 } } - \sqrt[ 3 ] { - 27 }$$

Evaluate

$$\frac{15}{2}=7.5$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$\sqrt{9}+\sqrt{\frac{2\times 4+1}{4}}-\sqrt[3]{-27}$$

Calculate the square root of 9 and get 3.

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

Multiply 2 and 4 to get 8.

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

Add 8 and 1 to get 9.

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

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.

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

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

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

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

$$\frac{9}{2}-\left(-3\right)$$

The opposite of -3 is 3.

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

Add \frac{9}{2} and 3 to get \frac{15}{2}.

$$\frac{15}{2}$$

Factor

$$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$$