Solve sqrt[3]{27/8}-sqrt[3]{1-189/64}-sqrt{1-31/256}

$$\sqrt[ 3 ] { \frac { 27 } { 8 } } - \sqrt[ 3 ] { 1 - \frac { 189 } { 64 } } - \sqrt { 1 - \frac { 31 } { 256 } }$$

Evaluate

$$\frac{29}{16}=1.8125$$

Solution Steps

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

$$\frac{3}{2}-\sqrt[3]{1-\frac{189}{64}}-\sqrt{1-\frac{31}{256}}$$

Subtract \frac{189}{64} from 1 to get -\frac{125}{64}.

$$\frac{3}{2}-\sqrt[3]{-\frac{125}{64}}-\sqrt{1-\frac{31}{256}}$$

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

$$\frac{3}{2}-\left(-\frac{5}{4}\right)-\sqrt{1-\frac{31}{256}}$$

The opposite of -\frac{5}{4} is \frac{5}{4}.

$$\frac{3}{2}+\frac{5}{4}-\sqrt{1-\frac{31}{256}}$$

Add \frac{3}{2} and \frac{5}{4} to get \frac{11}{4}.

$$\frac{11}{4}-\sqrt{1-\frac{31}{256}}$$

Subtract \frac{31}{256} from 1 to get \frac{225}{256}.

$$\frac{11}{4}-\sqrt{\frac{225}{256}}$$

Rewrite the square root of the division \frac{225}{256} as the division of square roots \frac{\sqrt{225}}{\sqrt{256}}. Take the square root of both numerator and denominator.

$$\frac{11}{4}-\frac{15}{16}$$

Subtract \frac{15}{16} from \frac{11}{4} to get \frac{29}{16}.

$$\frac{29}{16}$$

Factor

$$\frac{29}{2 ^ {4}} = 1\frac{13}{16} = 1.8125$$