First, we must figure out what $\displaystyle (x-y)$ is equal to.

We do $\displaystyle 3.09-2.97=0.12$.

Now to find out what $\displaystyle 0.12^2$ is equal to, we look at $\displaystyle 0.12\cdot 0.12$.

We move our decimal points over so that we are dealing with only whole numbers. This gives us $\displaystyle 12\cdot 12=144$.

Finally, we count how many spaces we moved our decimals in total, and we move the decimal in our answer back that many spaces. To get from $\displaystyle 0.12$ to $\displaystyle 12$ we moved our decimal two spaces to the right. Because we did this for each of the $\displaystyle 0.12$ values, our total spaces we moved the decimal was $\displaystyle 4$ to the right.

Therefore, we must take $\displaystyle 144$ and move the decimal $\displaystyle 4$ places to the left. This gives us $\displaystyle 0.0144$.

To solve, simply multiply 0.02 by 0.02 as though the numbers are without decimals.

Then, sum the number of spaces to the right of the decimal points in your problem and include that many in your answer.

Thus, your answer is .0004.

The easiest way to find the square root of a fraction is to convert it into scientific notation. 

$\displaystyle \dpi{100} \small .00081 = 8.1 \times 10^{-4}$

The key is that the exponent in scientific notation has to be even for a square root because the square root of an exponent is diving it by two. The square root of 9 is 3, so the square root of 8.1 is a little bit less than 3, around 2.8

 $\displaystyle \dpi{100} \small \sqrt{8.1 \times 10^{-4}} \approx 2.8 \times 10^{-2} \approx 0.028$

To find the square root of this decimal we convert it into scientific notation.

$\displaystyle \small 0.0049 = 49 \cdot10^{-4}$

Because $\displaystyle \small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root.

$\displaystyle \small \sqrt{0.0049} = \sqrt{49}\cdot\sqrt{10^{-4}} = 7\cdot10^{-2} = 0.07$

This problem can be solve more easily by rewriting the decimal into scientific notation.

$\displaystyle \small 0.025 = 2.5 \times 10^{-2}$

Because $\displaystyle \small 10^{-2}$ has an even exponent, we can take the square root of it by dividing it by 2. The square root of 4 is 2, and the square root of 1 is 1, so the square root of 2.5 is less than 2 and greater than 1.

$\displaystyle \small \sqrt{0.025} = \sqrt{2.5}\times \sqrt{10^{-2}} = 1.58\times 10^{-1} = 0.158$

This problem becomes much simpler if we rewrite the decimal in scientific notation

$\displaystyle \small 0.00036 = 3.6\times 10^{-4}$

Because $\displaystyle \small 10^{-4}$ has an even exponent, we can take its square root by dividing it by two. The square root of 4 is 2, and because 3.6 is a little smaller than 4, its square root is a little smaller than 2, around 1.9

$\displaystyle \small \sqrt{0.025} = \sqrt{3.6}\times \sqrt{10^{-4}} \approx 1.9\times 10^{-2} = 0.019$

To find the square root of this decimal we convert it into scientific notation.

$\displaystyle \small \small 0.00064 = 6.4 \times10^{-4}$

Because $\displaystyle \small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, and the square root of 4 is two, so the square root of 6.4 is between 3 and 2, around 2.53

$\displaystyle \small \small \sqrt{0.00064} = \sqrt{6.4}\times\sqrt{10^{-4}} \approx 2.53 \times10^{-2} = 0.0253$

To find the square root of this decimal we convert it into scientific notation.

$\displaystyle \small \small 0.0169 = 169\times10^{-4}$

Because $\displaystyle \small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root. $\displaystyle \small 169$ is a perfect square, whose square root is $\displaystyle \small 13$.

$\displaystyle \small \small \sqrt{0.0169} = \sqrt{169}\times \sqrt{10^{-4}} =13\times10^{-2} = 0.13$

To find the square root of this decimal we convert it into scientific notation.

$\displaystyle \small \small \small 0.00001 = 10 \times10^{-6}$

Because $\displaystyle \small \small 10^{-6}$ has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, so the square root of 10 should be a little larger than 3, around 3.16

$\displaystyle \small \small \sqrt{0.00001} = \sqrt{10}\times \sqrt{10^{-6}} = 3.16\times10^{-3} = 0.00316$

To find the square root of this decimal we convert it into scientific notation.

$\displaystyle \small \small 0.004 = 40 \times10^{-4}$

Because $\displaystyle \small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 36 is 6, so the square root of 40 should be a little more than 6, around 6.32. 

$\displaystyle \small \small \small \sqrt{0.004} = \sqrt{40}\times\sqrt{10^{-4}} \approx 6.32 \times10^{-2} = 0.0632$