Let's break down the expression step by step:
1. Start with the given values: [tex]\(a = 2\)[/tex] and [tex]\(b = -4\)[/tex].
2. First, calculate [tex]\(a^3 - 7\)[/tex]:
[tex]\[
a^3 - 7 = 2^3 - 7
\][/tex]
[tex]\[
2^3 = 8
\][/tex]
[tex]\[
8 - 7 = 1
\][/tex]
3. Next, take the square root of the result from step 2:
[tex]\[
\sqrt{1} = 1.0
\][/tex]
4. Now, find the absolute value of [tex]\(b\)[/tex]:
[tex]\[
|b| = |-4|
\][/tex]
[tex]\[
|b| = 4
\][/tex]
5. Finally, add the square root result (from step 3) to the absolute value of [tex]\(b\)[/tex] (from step 4):
[tex]\[
1.0 + 4 = 5.0
\][/tex]
So, when [tex]\(a = 2\)[/tex] and [tex]\(b = -4\)[/tex], the value of the expression [tex]\(\sqrt{a^3-7} + |b|\)[/tex] is [tex]\(5.0\)[/tex].
