Solve sqrt{2*10.7/9.7864}

$$\sqrt{ \frac{ 2 \times 10.7 }{ 9.7864 } }$$

Evaluate

$$\frac{5\sqrt{13089310}}{12233}\approx 1.478752205$$

Solution Steps

Multiply 2 and 10.7 to get 21.4.

$$\sqrt{\frac{21.4}{9.7864}}$$

Expand \frac{21.4}{9.7864} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{214000}{97864}}$$

Reduce the fraction \frac{214000}{97864} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{26750}{12233}}$$

Rewrite the square root of the division \sqrt{\frac{26750}{12233}} as the division of square roots \frac{\sqrt{26750}}{\sqrt{12233}}.

$$\frac{\sqrt{26750}}{\sqrt{12233}}$$

Factor 26750=5^{2}\times 1070. Rewrite the square root of the product \sqrt{5^{2}\times 1070} as the product of square roots \sqrt{5^{2}}\sqrt{1070}. Take the square root of 5^{2}.

$$\frac{5\sqrt{1070}}{\sqrt{12233}}$$

Rationalize the denominator of \frac{5\sqrt{1070}}{\sqrt{12233}} by multiplying numerator and denominator by \sqrt{12233}.

$$\frac{5\sqrt{1070}\sqrt{12233}}{\left(\sqrt{12233}\right)^{2}}$$

The square of \sqrt{12233} is 12233.

$$\frac{5\sqrt{1070}\sqrt{12233}}{12233}$$

To multiply \sqrt{1070} and \sqrt{12233}, multiply the numbers under the square root.

$$\frac{5\sqrt{13089310}}{12233}$$