Solve =sqrt{9.8/6.4*10^6}

$$= \sqrt { \frac { 9.8 } { 6.4 \times 10 ^ { 6 } } }$$

Evaluate

$$\frac{7\sqrt{2}}{8000}\approx 0.001237437$$

Solution Steps

Calculate 10 to the power of 6 and get 1000000.

$$\sqrt{\frac{9.8}{6.4\times 1000000}}$$

Multiply 6.4 and 1000000 to get 6400000.

$$\sqrt{\frac{9.8}{6400000}}$$

Expand \frac{9.8}{6400000} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{98}{64000000}}$$

Reduce the fraction \frac{98}{64000000} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{49}{32000000}}$$

Rewrite the square root of the division \sqrt{\frac{49}{32000000}} as the division of square roots \frac{\sqrt{49}}{\sqrt{32000000}}.

$$\frac{\sqrt{49}}{\sqrt{32000000}}$$

Calculate the square root of 49 and get 7.

$$\frac{7}{\sqrt{32000000}}$$

Factor 32000000=4000^{2}\times 2. Rewrite the square root of the product \sqrt{4000^{2}\times 2} as the product of square roots \sqrt{4000^{2}}\sqrt{2}. Take the square root of 4000^{2}.

$$\frac{7}{4000\sqrt{2}}$$

Rationalize the denominator of \frac{7}{4000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{7\sqrt{2}}{4000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{7\sqrt{2}}{4000\times 2}$$

Multiply 4000 and 2 to get 8000.

$$\frac{7\sqrt{2}}{8000}$$