Solve sqrt{(10/34)^3}

$$\sqrt { ( \frac { 10 } { 34 } ) ^ { 3 } }$$

Evaluate

$$\frac{5\sqrt{85}}{289}\approx 0.15950769$$

Solution Steps

Reduce the fraction \frac{10}{34} to lowest terms by extracting and canceling out 2.

$$\sqrt{\left(\frac{5}{17}\right)^{3}}$$

Calculate \frac{5}{17} to the power of 3 and get \frac{125}{4913}.

$$\sqrt{\frac{125}{4913}}$$

Rewrite the square root of the division \sqrt{\frac{125}{4913}} as the division of square roots \frac{\sqrt{125}}{\sqrt{4913}}.

$$\frac{\sqrt{125}}{\sqrt{4913}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\frac{5\sqrt{5}}{\sqrt{4913}}$$

Factor 4913=17^{2}\times 17. Rewrite the square root of the product \sqrt{17^{2}\times 17} as the product of square roots \sqrt{17^{2}}\sqrt{17}. Take the square root of 17^{2}.

$$\frac{5\sqrt{5}}{17\sqrt{17}}$$

Rationalize the denominator of \frac{5\sqrt{5}}{17\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{5\sqrt{5}\sqrt{17}}{17\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{5\sqrt{5}\sqrt{17}}{17\times 17}$$

To multiply \sqrt{5} and \sqrt{17}, multiply the numbers under the square root.

$$\frac{5\sqrt{85}}{17\times 17}$$

Multiply 17 and 17 to get 289.

$$\frac{5\sqrt{85}}{289}$$