Solve sqrt{10*2100*6,55/6,99}

$$\sqrt { \frac { 10 \times 2100 \times 6,55 } { 6,99 } }$$

Evaluate

$$\frac{50\sqrt{427322}}{233}\approx 140.278692566$$

Solution Steps

Multiply 10 and 2100 to get 21000.

$$\sqrt{\frac{21000\times 6,55}{6,99}}$$

Multiply 21000 and 6,55 to get 137550.

$$\sqrt{\frac{137550}{6,99}}$$

Expand \frac{137550}{6,99} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{13755000}{699}}$$

Reduce the fraction \frac{13755000}{699} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{4585000}{233}}$$

Rewrite the square root of the division \sqrt{\frac{4585000}{233}} as the division of square roots \frac{\sqrt{4585000}}{\sqrt{233}}.

$$\frac{\sqrt{4585000}}{\sqrt{233}}$$

Factor 4585000=50^{2}\times 1834. Rewrite the square root of the product \sqrt{50^{2}\times 1834} as the product of square roots \sqrt{50^{2}}\sqrt{1834}. Take the square root of 50^{2}.

$$\frac{50\sqrt{1834}}{\sqrt{233}}$$

Rationalize the denominator of \frac{50\sqrt{1834}}{\sqrt{233}} by multiplying numerator and denominator by \sqrt{233}.

$$\frac{50\sqrt{1834}\sqrt{233}}{\left(\sqrt{233}\right)^{2}}$$

The square of \sqrt{233} is 233.

$$\frac{50\sqrt{1834}\sqrt{233}}{233}$$

To multiply \sqrt{1834} and \sqrt{233}, multiply the numbers under the square root.

$$\frac{50\sqrt{427322}}{233}$$