What is the square roots of 0.0004?

3 Answers
Jun 6, 2018

Answer:

#0.02#

Explanation:

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#

Jun 6, 2018

Answer:

#+-0.02#

Explanation:

#"note that "100xx100=10000#

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

#0.0004=4/10000#

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

Jun 6, 2018

Answer:

#sqrt0.0004 =0.02#

Explanation:

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#