Solve sqrt{(0.004/0.968)^2+(0.008/5.465)^2}

$$\sqrt { ( \frac { 0.004 } { 0.968 } ) ^ { 2 } + ( \frac { 0.008 } { 5.465 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{33614321}}{1322530}\approx 0.00438386$$

Solution Steps

Expand \frac{0.004}{0.968} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\left(\frac{4}{968}\right)^{2}+\left(\frac{0.008}{5.465}\right)^{2}}$$

Reduce the fraction \frac{4}{968} to lowest terms by extracting and canceling out 4.

$$\sqrt{\left(\frac{1}{242}\right)^{2}+\left(\frac{0.008}{5.465}\right)^{2}}$$

Calculate \frac{1}{242} to the power of 2 and get \frac{1}{58564}.

$$\sqrt{\frac{1}{58564}+\left(\frac{0.008}{5.465}\right)^{2}}$$

Expand \frac{0.008}{5.465} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{1}{58564}+\left(\frac{8}{5465}\right)^{2}}$$

Calculate \frac{8}{5465} to the power of 2 and get \frac{64}{29866225}.

$$\sqrt{\frac{1}{58564}+\frac{64}{29866225}}$$

Add \frac{1}{58564} and \frac{64}{29866225} to get \frac{33614321}{1749085600900}.

$$\sqrt{\frac{33614321}{1749085600900}}$$

Rewrite the square root of the division \sqrt{\frac{33614321}{1749085600900}} as the division of square roots \frac{\sqrt{33614321}}{\sqrt{1749085600900}}.

$$\frac{\sqrt{33614321}}{\sqrt{1749085600900}}$$

Calculate the square root of 1749085600900 and get 1322530.

$$\frac{\sqrt{33614321}}{1322530}$$