Solve sqrt{3.088/3.4}

$$\sqrt{ \frac{ 3.088 }{ 3.4 } }$$

Evaluate

$$\frac{\sqrt{6562}}{85}\approx 0.953013795$$

Solution Steps

Expand \frac{3.088}{3.4} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{3088}{3400}}$$

Reduce the fraction \frac{3088}{3400} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{386}{425}}$$

Rewrite the square root of the division \sqrt{\frac{386}{425}} as the division of square roots \frac{\sqrt{386}}{\sqrt{425}}.

$$\frac{\sqrt{386}}{\sqrt{425}}$$

Factor 425=5^{2}\times 17. Rewrite the square root of the product \sqrt{5^{2}\times 17} as the product of square roots \sqrt{5^{2}}\sqrt{17}. Take the square root of 5^{2}.

$$\frac{\sqrt{386}}{5\sqrt{17}}$$

Rationalize the denominator of \frac{\sqrt{386}}{5\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{\sqrt{386}\sqrt{17}}{5\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{\sqrt{386}\sqrt{17}}{5\times 17}$$

To multiply \sqrt{386} and \sqrt{17}, multiply the numbers under the square root.

$$\frac{\sqrt{6562}}{5\times 17}$$

Multiply 5 and 17 to get 85.

$$\frac{\sqrt{6562}}{85}$$