To find the value of the expression [tex]\(\sqrt{a^3 - 7} + |b|\)[/tex] when [tex]\(a = 2\)[/tex] and [tex]\(b = -4\)[/tex], let's go through the steps:
1. Substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the expression:
[tex]\[
a = 2 \quad \text{and} \quad b = -4
\][/tex]
2. Evaluate the term [tex]\(a^3\)[/tex]:
[tex]\[
2^3 = 8
\][/tex]
3. Subtract 7 from [tex]\(a^3\)[/tex]:
[tex]\[
8 - 7 = 1
\][/tex]
4. Find the square root of the result:
[tex]\[
\sqrt{1} = 1
\][/tex]
5. Calculate the absolute value of [tex]\(b\)[/tex]:
[tex]\[
| -4 | = 4
\][/tex]
6. Add the results from steps 4 and 5:
[tex]\[
1 + 4 = 5
\][/tex]
Thus, 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].
