Solve sqrt{2*1*9.81/0.45*0.07*1.23}

$$\sqrt{ \frac{ 2 \cdot 1 \cdot 9.81 }{ 0.45 \cdot 0.07 \times 1.23 } }$$

Evaluate

$$\frac{20\sqrt{938490}}{861}\approx 22.503064703$$

Solution Steps

Multiply 2 and 1 to get 2.

$$\sqrt{\frac{2\times 9.81}{0.45\times 0.07\times 1.23}}$$

Multiply 2 and 9.81 to get 19.62.

$$\sqrt{\frac{19.62}{0.45\times 0.07\times 1.23}}$$

Multiply 0.45 and 0.07 to get 0.0315.

$$\sqrt{\frac{19.62}{0.0315\times 1.23}}$$

Multiply 0.0315 and 1.23 to get 0.038745.

$$\sqrt{\frac{19.62}{0.038745}}$$

Expand \frac{19.62}{0.038745} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{19620000}{38745}}$$

Reduce the fraction \frac{19620000}{38745} to lowest terms by extracting and canceling out 45.

$$\sqrt{\frac{436000}{861}}$$

Rewrite the square root of the division \sqrt{\frac{436000}{861}} as the division of square roots \frac{\sqrt{436000}}{\sqrt{861}}.

$$\frac{\sqrt{436000}}{\sqrt{861}}$$

Factor 436000=20^{2}\times 1090. Rewrite the square root of the product \sqrt{20^{2}\times 1090} as the product of square roots \sqrt{20^{2}}\sqrt{1090}. Take the square root of 20^{2}.

$$\frac{20\sqrt{1090}}{\sqrt{861}}$$

Rationalize the denominator of \frac{20\sqrt{1090}}{\sqrt{861}} by multiplying numerator and denominator by \sqrt{861}.

$$\frac{20\sqrt{1090}\sqrt{861}}{\left(\sqrt{861}\right)^{2}}$$

The square of \sqrt{861} is 861.

$$\frac{20\sqrt{1090}\sqrt{861}}{861}$$

To multiply \sqrt{1090} and \sqrt{861}, multiply the numbers under the square root.

$$\frac{20\sqrt{938490}}{861}$$