Solve sqrt[3]{33/8}+sqrt{1/4}-sqrt{25}

$$\sqrt[ 3 ] { 3 \frac { 3 } { 8 } } + \sqrt { \frac { 1 } { 4 } } - \sqrt { 25 }$$

Evaluate

$$-3$$

Solution Steps

Multiply 3 and 8 to get 24.

$$\sqrt[3]{\frac{24+3}{8}}+\sqrt{\frac{1}{4}}-\sqrt{25}$$

Add 24 and 3 to get 27.

$$\sqrt[3]{\frac{27}{8}}+\sqrt{\frac{1}{4}}-\sqrt{25}$$

Calculate \sqrt[3]{\frac{27}{8}} and get \frac{3}{2}.

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

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.

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

Add \frac{3}{2} and \frac{1}{2} to get 2.

$$2-\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$2-5$$

Subtract 5 from 2 to get -3.

$$-3$$

Factor

$$-3$$