Solve sqrt{1}-sqrt{7/9}+sqrt[3]{-27}

$$\sqrt { 1 } - \sqrt { \frac { 7 } { 9 } } + \sqrt[ 3 ] { - 27 }$$

Evaluate

$$-\frac{\sqrt{7}}{3}-2\approx -2.881917104$$

Short Solution Steps

Calculate the square root of 1 and get 1.

$$1-\sqrt{\frac{7}{9}}+\sqrt[3]{-27}$$

Rewrite the square root of the division \sqrt{\frac{7}{9}} as the division of square roots \frac{\sqrt{7}}{\sqrt{9}}.

$$1-\frac{\sqrt{7}}{\sqrt{9}}+\sqrt[3]{-27}$$

Calculate the square root of 9 and get 3.

$$1-\frac{\sqrt{7}}{3}+\sqrt[3]{-27}$$

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

$$1-\frac{\sqrt{7}}{3}-3$$

Subtract 3 from 1 to get -2.

$$-2-\frac{\sqrt{7}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2 times \frac{3}{3}.

$$-\frac{2\times 3}{3}-\frac{\sqrt{7}}{3}$$

Since -\frac{2\times 3}{3} and \frac{\sqrt{7}}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2\times 3-\sqrt{7}}{3}$$

Do the multiplications in -2\times 3-\sqrt{7}.

$$\frac{-6-\sqrt{7}}{3}$$