Solve sqrt{(1400-83*9,8)*52/83}

$$\sqrt { \frac { ( 1400 - 83 \times 9,8 ) \times 52 } { 83 } }$$

Evaluate

$$\frac{2\sqrt{15823535}}{415}\approx 19.17050948$$

Solution Steps

Multiply 83 and 9,8 to get 813,4.

$$\sqrt{\frac{\left(1400-813,4\right)\times 52}{83}}$$

Subtract 813,4 from 1400 to get 586,6.

$$\sqrt{\frac{586,6\times 52}{83}}$$

Multiply 586,6 and 52 to get 30503,2.

$$\sqrt{\frac{30503,2}{83}}$$

Expand \frac{30503,2}{83} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{305032}{830}}$$

Reduce the fraction \frac{305032}{830} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{152516}{415}}$$

Rewrite the square root of the division \sqrt{\frac{152516}{415}} as the division of square roots \frac{\sqrt{152516}}{\sqrt{415}}.

$$\frac{\sqrt{152516}}{\sqrt{415}}$$

Factor 152516=2^{2}\times 38129. Rewrite the square root of the product \sqrt{2^{2}\times 38129} as the product of square roots \sqrt{2^{2}}\sqrt{38129}. Take the square root of 2^{2}.

$$\frac{2\sqrt{38129}}{\sqrt{415}}$$

Rationalize the denominator of \frac{2\sqrt{38129}}{\sqrt{415}} by multiplying numerator and denominator by \sqrt{415}.

$$\frac{2\sqrt{38129}\sqrt{415}}{\left(\sqrt{415}\right)^{2}}$$

The square of \sqrt{415} is 415.

$$\frac{2\sqrt{38129}\sqrt{415}}{415}$$

To multiply \sqrt{38129} and \sqrt{415}, multiply the numbers under the square root.

$$\frac{2\sqrt{15823535}}{415}$$