Solve sqrt[3]{-125/64}+sqrt{1-7/16}-sqrt[3]{-343/8}

$$\sqrt[ 3 ] { - \frac { 125 } { 64 } } + \sqrt { 1 - \frac { 7 } { 16 } } - \sqrt[ 3 ] { - \frac { 343 } { 8 } }$$

Evaluate

$$3$$

Solution Steps

Calculate \sqrt[3]{-\frac{125}{64}} and get -\frac{5}{4}.

$$-\frac{5}{4}+\sqrt{1-\frac{7}{16}}-\sqrt[3]{-\frac{343}{8}}$$

Subtract \frac{7}{16} from 1 to get \frac{9}{16}.

$$-\frac{5}{4}+\sqrt{\frac{9}{16}}-\sqrt[3]{-\frac{343}{8}}$$

Rewrite the square root of the division \frac{9}{16} as the division of square roots \frac{\sqrt{9}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$-\frac{5}{4}+\frac{3}{4}-\sqrt[3]{-\frac{343}{8}}$$

Add -\frac{5}{4} and \frac{3}{4} to get -\frac{1}{2}.

$$-\frac{1}{2}-\sqrt[3]{-\frac{343}{8}}$$

Calculate \sqrt[3]{-\frac{343}{8}} and get -\frac{7}{2}.

$$-\frac{1}{2}-\left(-\frac{7}{2}\right)$$

The opposite of -\frac{7}{2} is \frac{7}{2}.

$$-\frac{1}{2}+\frac{7}{2}$$

Add -\frac{1}{2} and \frac{7}{2} to get 3.

$$3$$

Factor

$$3$$