Solve sqrt{27x^18/49x^18}

$$\sqrt { \frac { 27 x ^ { 18 } } { 49 x ^ { 18 } } }$$

Evaluate

$$\frac{3\sqrt{3}}{7}\approx 0.742307489$$

Solution Steps

Cancel out x^{18} in both numerator and denominator.

$$\sqrt{\frac{27}{49}}$$

Rewrite the square root of the division \sqrt{\frac{27}{49}} as the division of square roots \frac{\sqrt{27}}{\sqrt{49}}.

$$\frac{\sqrt{27}}{\sqrt{49}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{3\sqrt{3}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

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