Let's go step-by-step to compute the square roots of the given numbers: [tex]\(-2\)[/tex], [tex]\(0\)[/tex], [tex]\(3\)[/tex], [tex]\(5\)[/tex], and [tex]\(-4\)[/tex].
1. Square Root of [tex]\(-2\)[/tex]:
- The square root of a negative number is not defined in the set of real numbers. Therefore, [tex]\(\sqrt{-2}\)[/tex] is undefined for negative numbers in the real number system.
2. Square Root of [tex]\(0\)[/tex]:
- The square root of [tex]\(0\)[/tex] is 0 because [tex]\(0 \times 0 = 0\)[/tex].
[tex]\[
\sqrt{0} = 0.0
\][/tex]
3. Square Root of [tex]\(3\)[/tex]:
- To find the square root of [tex]\(3\)[/tex], recognize it as a non-perfect square. The exact value is an irrational number.
[tex]\[
\sqrt{3} \approx 1.7320508075688772
\][/tex]
4. Square Root of [tex]\(5\)[/tex]:
- Similarly, the square root of [tex]\(5\)[/tex] is an irrational number.
[tex]\[
\sqrt{5} \approx 2.23606797749979
\][/tex]
5. Square Root of [tex]\(-4\)[/tex]:
- Like [tex]\(\sqrt{-2}\)[/tex], the square root of a negative number is undefined in the set of real numbers.
[tex]\[
\sqrt{-4} \; \text{is undefined for negative numbers}
\][/tex]
Let us summarize our results:
- [tex]\(\sqrt{-2}\)[/tex] is undefined for negative numbers.
- [tex]\(\sqrt{0} = 0.0\)[/tex].
- [tex]\(\sqrt{3} \approx 1.7320508075688772\)[/tex].
- [tex]\(\sqrt{5} \approx 2.23606797749979\)[/tex].
- [tex]\(\sqrt{-4}\)[/tex] is undefined for negative numbers.
Thus, the detailed solutions for the given numbers are:
[tex]\[
\sqrt{-2}, \sqrt{0}, \sqrt{3}, \sqrt{5}, \sqrt{-4} \implies (\text{undefined for negative}, 0.0, 1.7320508075688772, 2.23606797749979, \text{undefined for negative})
\][/tex]
