Solve sqrt{(0.2*9*9.8*0.1+0.5)*18/0.02}

$$\sqrt { \frac { ( 0.2 \times 9 \times 9.8 \times 0.1 + 0.5 ) \times 18 } { 0.02 } }$$

Evaluate

$$\frac{6\sqrt{1415}}{5}\approx 45.139782897$$

Solution Steps

Multiply 0.2 and 9 to get 1.8.

$$\sqrt{\frac{\left(1.8\times 9.8\times 0.1+0.5\right)\times 18}{0.02}}$$

Multiply 1.8 and 9.8 to get 17.64.

$$\sqrt{\frac{\left(17.64\times 0.1+0.5\right)\times 18}{0.02}}$$

Multiply 17.64 and 0.1 to get 1.764.

$$\sqrt{\frac{\left(1.764+0.5\right)\times 18}{0.02}}$$

Add 1.764 and 0.5 to get 2.264.

$$\sqrt{\frac{2.264\times 18}{0.02}}$$

Multiply 2.264 and 18 to get 40.752.

$$\sqrt{\frac{40.752}{0.02}}$$

Expand \frac{40.752}{0.02} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{40752}{20}}$$

Reduce the fraction \frac{40752}{20} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{10188}{5}}$$

Rewrite the square root of the division \sqrt{\frac{10188}{5}} as the division of square roots \frac{\sqrt{10188}}{\sqrt{5}}.

$$\frac{\sqrt{10188}}{\sqrt{5}}$$

Factor 10188=6^{2}\times 283. Rewrite the square root of the product \sqrt{6^{2}\times 283} as the product of square roots \sqrt{6^{2}}\sqrt{283}. Take the square root of 6^{2}.

$$\frac{6\sqrt{283}}{\sqrt{5}}$$

Rationalize the denominator of \frac{6\sqrt{283}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{6\sqrt{283}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{6\sqrt{283}\sqrt{5}}{5}$$

To multiply \sqrt{283} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{6\sqrt{1415}}{5}$$