Solve -frac{sqrt{72}}{7sqrt{18}}

$$- \frac { \sqrt { 72 } } { 7 \sqrt { 18 } }$$

Evaluate

$$-\frac{2}{7}\approx -0.285714286$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$-\frac{6\sqrt{2}}{7\sqrt{18}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$-\frac{6\sqrt{2}}{7\times 3\sqrt{2}}$$

Multiply 7 and 3 to get 21.

$$-\frac{6\sqrt{2}}{21\sqrt{2}}$$

Cancel out 3\sqrt{2} in both numerator and denominator.

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

Factor

$$-\frac{2}{7} = -0.2857142857142857$$