Solve sqrt{25.49/6}

$$\sqrt{ \frac{ 25.49 }{ 6 } }$$

Evaluate

$$\frac{\sqrt{15294}}{60}\approx 2.061148547$$

Solution Steps

Expand \frac{25.49}{6} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{2549}{600}}$$

Rewrite the square root of the division \sqrt{\frac{2549}{600}} as the division of square roots \frac{\sqrt{2549}}{\sqrt{600}}.

$$\frac{\sqrt{2549}}{\sqrt{600}}$$

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$\frac{\sqrt{2549}}{10\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{2549}}{10\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{2549}\sqrt{6}}{10\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{2549}\sqrt{6}}{10\times 6}$$

To multiply \sqrt{2549} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{15294}}{10\times 6}$$

Multiply 10 and 6 to get 60.

$$\frac{\sqrt{15294}}{60}$$