Let's evaluate the expression [tex]\(\sqrt{a^3-7} + |b|\)[/tex] step-by-step, given [tex]\(a = 2\)[/tex] and [tex]\(b = -4\)[/tex].
1. Calculate [tex]\(a^3\)[/tex]:
[tex]\[
2^3 = 8
\][/tex]
2. Subtract 7 from [tex]\(a^3\)[/tex]:
[tex]\[
8 - 7 = 1
\][/tex]
3. Take the square root of the result:
[tex]\[
\sqrt{1} = 1.0
\][/tex]
4. Determine the absolute value of [tex]\(b\)[/tex]:
[tex]\[
| -4 | = 4
\][/tex]
5. Finally, add the results:
[tex]\[
1.0 + 4 = 5.0
\][/tex]
Therefore, the value of the expression [tex]\(\sqrt{a^3-7} + |b|\)[/tex] when [tex]\(a = 2\)[/tex] and [tex]\(b = -4\)[/tex] is [tex]\(5.0\)[/tex].
