Solve sqrt{2*9.8*50*10^-2}

$$\sqrt{ 2 \times 9.8 \times 50 \times { 10 }^{ -2 } }$$

Evaluate

$$\frac{7\sqrt{5}}{5}\approx 3.130495168$$

Solution Steps

Multiply 2 and 9.8 to get 19.6.

$$\sqrt{19.6\times 50\times 10^{-2}}$$

Multiply 19.6 and 50 to get 980.

$$\sqrt{980\times 10^{-2}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\sqrt{980\times \frac{1}{100}}$$

Multiply 980 and \frac{1}{100} to get \frac{49}{5}.

$$\sqrt{\frac{49}{5}}$$

Rewrite the square root of the division \sqrt{\frac{49}{5}} as the division of square roots \frac{\sqrt{49}}{\sqrt{5}}.

$$\frac{\sqrt{49}}{\sqrt{5}}$$

Calculate the square root of 49 and get 7.

$$\frac{7}{\sqrt{5}}$$

Rationalize the denominator of \frac{7}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{7\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{7\sqrt{5}}{5}$$