Let's evaluate the given expression step by step with the values [tex]\( a = 2 \)[/tex] and [tex]\( b = -4 \)[/tex].
Given expression:
[tex]\[
\sqrt{a^3 - 7} + |b|
\][/tex]
Step 1: Compute [tex]\( a^3 \)[/tex].
Given [tex]\( a = 2 \)[/tex]:
[tex]\[
a^3 = 2^3 = 8
\][/tex]
Step 2: Substitute [tex]\( a^3 \)[/tex] back into the expression.
[tex]\[
\sqrt{8 - 7} + |b|
\][/tex]
Step 3: Simplify [tex]\( 8 - 7 \)[/tex].
[tex]\[
8 - 7 = 1
\][/tex]
So the expression now becomes:
[tex]\[
\sqrt{1} + |b|
\][/tex]
Step 4: Compute the square root of 1.
[tex]\[
\sqrt{1} = 1
\][/tex]
Step 5: Calculate the absolute value of [tex]\( b \)[/tex].
Given [tex]\( b = -4 \)[/tex]:
[tex]\[
|b| = |-4| = 4
\][/tex]
Step 6: Substitute the calculated values into the expression.
[tex]\[
1 + 4
\][/tex]
Step 7: Add the values together.
[tex]\[
1 + 4 = 5
\][/tex]
Therefore, the value of the expression is:
[tex]\[
\boxed{5}
\][/tex]
