Sure, let's solve the given expression step by step:
Given the expression:
[tex]\[ \sqrt{a^3 - 7} + |b| \][/tex]
where [tex]\( a = 2 \)[/tex] and [tex]\( b = -4 \)[/tex].
1. Calculate [tex]\( a^3 \)[/tex]:
[tex]\[ a^3 = 2^3 = 8 \][/tex]
2. Substitute [tex]\( a^3 \)[/tex] into the expression:
[tex]\[ a^3 - 7 = 8 - 7 = 1 \][/tex]
3. Calculate the square root:
[tex]\[ \sqrt{1} = 1.0 \][/tex]
4. Calculate the absolute value of [tex]\( b \)[/tex]:
[tex]\[ |b| = |-4| = 4 \][/tex]
5. Add the results together:
[tex]\[ \sqrt{1} + |b| = 1.0 + 4 = 5.0 \][/tex]
Therefore, when [tex]\( a = 2 \)[/tex] and [tex]\( b = -4 \)[/tex], the value of the expression is [tex]\( \boxed{5.0} \)[/tex].
