What is the square roots of 0.0004?

It can help to write the number in scientific notation:

`0.0004 = 4*10^-4`

The square root of a product is the product of the square roots:

`sqrt(4*10^-4) = sqrt(4)*sqrt(10^{-4})`

Now, `sqrt(4)` is easily `2`. As for the exponential part, taking the square root is the same as giving exponent `1/2`:

`sqrt(10^{-4}) = (10^{-4})^{1/2}`

Now use the property `(a^b)^c = a^{bc}` to get

`(10^{-4})^{1/2} = 10^{-4/2} = 10^{-2}`

So, the answer is `2*10^{-2}`, or if you prefer `0.02`

`"note that "100xx100=10000`

`"and "(-100)xx(-100)=10000`

`0.0004=4/10000`

`rArrsqrt(0.0004)=sqrt(4/10000)=+-2/100=+-0.02`

To find the square root of a number:

• group the digits into pairs, starting from the decimal point.

• The number of pairs is the same as the number of place holders in the square root.

• find the square root

`sqrt 100 = sqrt((color(blue)(1)" "color(green)(00))) =color(blue)(1)color(green)(0) = 10`

`sqrt16900 = sqrt(color(blue)(1)color(green)(69)" "color(red)(00)) = color(blue)(1)color(green)(3)" "color(red)(0) = 130`

`sqrt0.000001= sqrt(0color(blue)(.00)" "color(green)(00)" "color(red)(01)) = 0color(blue)(.0)" "color(green)(0)" "color(red)(1) = 0.001`

`sqrt0.0004 = sqrt(0color(blue)(.00)" "color(green)(04)) = 0color(blue)(.0)" "color(green)(2) =0.02`