Solve -6sqrt{8/9}

$$- 6 \sqrt { \frac { 8 } { 9 } }$$

Evaluate

$$-4\sqrt{2}\approx -5.656854249$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{8}{9}} as the division of square roots \frac{\sqrt{8}}{\sqrt{9}}.

$$-6\times \frac{\sqrt{8}}{\sqrt{9}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$-6\times \frac{2\sqrt{2}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$-6\times \frac{2\sqrt{2}}{3}$$

Cancel out 3, the greatest common factor in 6 and 3.

$$-2\times 2\sqrt{2}$$

Multiply -2 and 2 to get -4.

$$-4\sqrt{2}$$