Solve sqrt{864.2/9}

$$\sqrt{ \frac{ 864.2 }{ 9 } }$$

Evaluate

$$\frac{\sqrt{21605}}{15}\approx 9.799092929$$

Solution Steps

Expand \frac{864.2}{9} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{8642}{90}}$$

Reduce the fraction \frac{8642}{90} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{4321}{45}}$$

Rewrite the square root of the division \sqrt{\frac{4321}{45}} as the division of square roots \frac{\sqrt{4321}}{\sqrt{45}}.

$$\frac{\sqrt{4321}}{\sqrt{45}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{\sqrt{4321}}{3\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{4321}}{3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{4321}\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{4321}\sqrt{5}}{3\times 5}$$

To multiply \sqrt{4321} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{21605}}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{\sqrt{21605}}{15}$$