Solve 0.6/2*sqrt{25*9.8}=

$$\frac { 0.6 } { 2 \times \sqrt { 25 \times 9.8 } } =$$

Evaluate

$$\frac{3\sqrt{5}}{350}\approx 0.019166297$$

Solution Steps

Multiply 25 and 9.8 to get 245.

$$\frac{0.6}{2\sqrt{245}}$$

Factor 245=7^{2}\times 5. Rewrite the square root of the product \sqrt{7^{2}\times 5} as the product of square roots \sqrt{7^{2}}\sqrt{5}. Take the square root of 7^{2}.

$$\frac{0.6}{2\times 7\sqrt{5}}$$

Multiply 2 and 7 to get 14.

$$\frac{0.6}{14\sqrt{5}}$$

Rationalize the denominator of \frac{0.6}{14\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{0.6\sqrt{5}}{14\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{0.6\sqrt{5}}{14\times 5}$$

Multiply 14 and 5 to get 70.

$$\frac{0.6\sqrt{5}}{70}$$

Divide 0.6\sqrt{5} by 70 to get \frac{3}{350}\sqrt{5}.

$$\frac{3}{350}\sqrt{5}$$