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]\[
\sqrt{1} = 1
\][/tex]
4. Find the absolute value of [tex]\(b\)[/tex]:
[tex]\[
|b| = |-4| = 4
\][/tex]
5. Add the two results together:
[tex]\[
\sqrt{1} + |b| = 1 + 4 = 5
\][/tex]
Therefore, when [tex]\(a = 2\)[/tex] and [tex]\(b = -4\)[/tex], the value of the expression is [tex]\(5.0\)[/tex].
