1. Find all the real square roots of
a. .0064
b. - .0081
don't you recognize 8^2 and 9^2 ?
a. To find the real square roots of 0.0064, we can take the square root of the absolute value of the number, and then consider the sign separately.
First, let's find the square root of the absolute value of 0.0064:
√(0.0064) ≈ 0.080
Now, let's consider the sign. Since the number is positive (0.0064), there is only one real square root:
√(0.0064) ≈ 0.080
Therefore, the only real square root of 0.0064 is approximately 0.080.
b. To find the real square roots of -0.0081, we can follow a similar process. However, because the number is negative, there are no real square roots.
Therefore, there are no real square roots of -0.0081.
To find the real square roots of a number, we need to find the numbers that, when multiplied by themselves, give the given number as a result.
a. For the number 0.0064, we can find its square root by taking the square root of the absolute value of the number and adding a positive/negative sign according to the original number.
The square root of 0.0064 is √(0.0064), which is approximately 0.08. Since we are looking for the real square roots, we have one positive square root: 0.08.
b. For the number -0.0081, we cannot find a real square root since the square root of a negative number is not a real number. However, we can find the imaginary square roots by converting the negative number into its absolute value and taking the square root.
The square root of |-0.0081| is √(0.0081), which is approximately 0.09. Since we are looking for the imaginary square roots, we have two imaginary square roots: ±0.09i.
In summary:
a. Real square root of 0.0064: 0.08
b. Imaginary square roots of -0.0081: ±0.09i