Solve sqrt{1.8288/9.8*2}

$$\sqrt{ \frac{ 1.8288 }{ 9.8 } \times 2 }$$

Evaluate

$$\frac{3\sqrt{1270}}{175}\approx 0.610921018$$

Solution Steps

Expand \frac{1.8288}{9.8} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{18288}{98000}\times 2}$$

Reduce the fraction \frac{18288}{98000} to lowest terms by extracting and canceling out 16.

$$\sqrt{\frac{1143}{6125}\times 2}$$

Express \frac{1143}{6125}\times 2 as a single fraction.

$$\sqrt{\frac{1143\times 2}{6125}}$$

Multiply 1143 and 2 to get 2286.

$$\sqrt{\frac{2286}{6125}}$$

Rewrite the square root of the division \sqrt{\frac{2286}{6125}} as the division of square roots \frac{\sqrt{2286}}{\sqrt{6125}}.

$$\frac{\sqrt{2286}}{\sqrt{6125}}$$

Factor 2286=3^{2}\times 254. Rewrite the square root of the product \sqrt{3^{2}\times 254} as the product of square roots \sqrt{3^{2}}\sqrt{254}. Take the square root of 3^{2}.

$$\frac{3\sqrt{254}}{\sqrt{6125}}$$

Factor 6125=35^{2}\times 5. Rewrite the square root of the product \sqrt{35^{2}\times 5} as the product of square roots \sqrt{35^{2}}\sqrt{5}. Take the square root of 35^{2}.

$$\frac{3\sqrt{254}}{35\sqrt{5}}$$

Rationalize the denominator of \frac{3\sqrt{254}}{35\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\sqrt{254}\sqrt{5}}{35\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{254}\sqrt{5}}{35\times 5}$$

To multiply \sqrt{254} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{3\sqrt{1270}}{35\times 5}$$

Multiply 35 and 5 to get 175.

$$\frac{3\sqrt{1270}}{175}$$