Solve -4/27-sqrt{7/9}:9/7=

$$- \frac { 4 } { 27 } - \sqrt { \frac { 7 } { 9 } } : \frac { 9 } { 7 } =$$

Evaluate

$$\frac{-7\sqrt{7}-4}{27}\approx -0.834083673$$

Short Solution Steps

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

$$-\frac{4}{27}-\frac{\frac{\sqrt{7}}{\sqrt{9}}}{\frac{9}{7}}$$

Calculate the square root of 9 and get 3.

$$-\frac{4}{27}-\frac{\frac{\sqrt{7}}{3}}{\frac{9}{7}}$$

Divide \frac{\sqrt{7}}{3} by \frac{9}{7} by multiplying \frac{\sqrt{7}}{3} by the reciprocal of \frac{9}{7}.

$$-\frac{4}{27}-\frac{\sqrt{7}\times 7}{3\times 9}$$

Multiply 3 and 9 to get 27.

$$-\frac{4}{27}-\frac{\sqrt{7}\times 7}{27}$$

Since -\frac{4}{27} and \frac{\sqrt{7}\times 7}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4-\sqrt{7}\times 7}{27}$$

Do the multiplications in -4-\sqrt{7}\times 7.

$$\frac{-4-7\sqrt{7}}{27}$$

Factor

$$\frac{-7 \sqrt{7} - 4}{27} = -0.834083673238968$$