Sure, let’s find the square roots of the given numbers: [tex]\( -2, 0, 3, 5, \)[/tex] and [tex]\( -4 \)[/tex].
### Step-by-Step Solution:
1. Find the square root of [tex]\(-2\)[/tex]:
[tex]\[
\sqrt{-2} = \sqrt{2} \cdot \sqrt{-1} = \sqrt{2} \cdot i \approx 1.4142135623730951 \cdot i
\][/tex]
This is a complex number written as [tex]\( 1.4142135623730951i \)[/tex].
2. Find the square root of [tex]\(0\)[/tex]:
[tex]\[
\sqrt{0} = 0
\][/tex]
3. Find the square root of [tex]\(3\)[/tex]:
[tex]\[
\sqrt{3} \approx 1.7320508075688772
\][/tex]
4. Find the square root of [tex]\(5\)[/tex]:
[tex]\[
\sqrt{5} \approx 2.23606797749979
\][/tex]
5. Find the square root of [tex]\(-4\)[/tex]:
[tex]\[
\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2 \cdot i = 2i
\][/tex]
This is a complex number written as [tex]\( 2i \)[/tex].
### Final Numerical Results:
[tex]\[
\sqrt{-2} \approx 1.4142135623730951i, \quad \sqrt{0} = 0, \quad \sqrt{3} \approx 1.7320508075688772, \quad \sqrt{5} \approx 2.23606797749979, \quad \sqrt{-4} = 2i
\][/tex]
So, the values are:
[tex]\[
(1.4142135623730951+0j), 0.0, 1.7320508075688772, 2.23606797749979, (2+0j)
\][/tex]
