To find the value of the expression [tex]\(\sqrt{a^3 - 7} + |b|\)[/tex] when [tex]\(a = 2\)[/tex] and [tex]\(b = -4\)[/tex], follow these steps:
1. Calculate [tex]\(a^3\)[/tex].
[tex]\[
a^3 = 2^3 = 8
\][/tex]
2. Subtract 7 from [tex]\(a^3\)[/tex].
[tex]\[
a^3 - 7 = 8 - 7 = 1
\][/tex]
3. Take the square root of the result.
[tex]\[
\sqrt{1} = 1.0
\][/tex]
4. Find the absolute value of [tex]\(b\)[/tex].
[tex]\[
|b| = |-4| = 4
\][/tex]
5. Add the result from step 3 and step 4.
[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]\(\boxed{5.0}\)[/tex].
