Solve sqrt{7.8496.27^2/19.863}

$$\sqrt{ \frac{ 7.849 { 6.27 }^{ 2 } }{ 19.863 } }$$

Evaluate

$$\frac{209\sqrt{17322743}}{220700}\approx 3.94141608$$

Solution Steps

Calculate 6.27 to the power of 2 and get 39.3129.

$$\sqrt{\frac{7.849\times 39.3129}{19.863}}$$

Multiply 7.849 and 39.3129 to get 308.5669521.

$$\sqrt{\frac{308.5669521}{19.863}}$$

Expand \frac{308.5669521}{19.863} by multiplying both numerator and the denominator by 10000000.

$$\sqrt{\frac{3085669521}{198630000}}$$

Reduce the fraction \frac{3085669521}{198630000} to lowest terms by extracting and canceling out 9.

$$\sqrt{\frac{342852169}{22070000}}$$

Rewrite the square root of the division \sqrt{\frac{342852169}{22070000}} as the division of square roots \frac{\sqrt{342852169}}{\sqrt{22070000}}.

$$\frac{\sqrt{342852169}}{\sqrt{22070000}}$$

Factor 342852169=209^{2}\times 7849. Rewrite the square root of the product \sqrt{209^{2}\times 7849} as the product of square roots \sqrt{209^{2}}\sqrt{7849}. Take the square root of 209^{2}.

$$\frac{209\sqrt{7849}}{\sqrt{22070000}}$$

Factor 22070000=100^{2}\times 2207. Rewrite the square root of the product \sqrt{100^{2}\times 2207} as the product of square roots \sqrt{100^{2}}\sqrt{2207}. Take the square root of 100^{2}.

$$\frac{209\sqrt{7849}}{100\sqrt{2207}}$$

Rationalize the denominator of \frac{209\sqrt{7849}}{100\sqrt{2207}} by multiplying numerator and denominator by \sqrt{2207}.

$$\frac{209\sqrt{7849}\sqrt{2207}}{100\left(\sqrt{2207}\right)^{2}}$$

The square of \sqrt{2207} is 2207.

$$\frac{209\sqrt{7849}\sqrt{2207}}{100\times 2207}$$

To multiply \sqrt{7849} and \sqrt{2207}, multiply the numbers under the square root.

$$\frac{209\sqrt{17322743}}{100\times 2207}$$

Multiply 100 and 2207 to get 220700.

$$\frac{209\sqrt{17322743}}{220700}$$