Let's solve the given expression step-by-step:
Given:
[tex]\[ \sqrt{a^3 - 7} + |3| \][/tex]
We need to find the value of the expression when [tex]\( a = 2 \)[/tex].
First, calculate [tex]\( a^3 \)[/tex]:
[tex]\[ a^3 = 2^3 = 8 \][/tex]
Next, substitute [tex]\( a^3 \)[/tex] into the expression [tex]\( a^3 - 7 \)[/tex]:
[tex]\[ 8 - 7 = 1 \][/tex]
Now compute the square root of the result:
[tex]\[ \sqrt{1} = 1.0 \][/tex]
Next, compute the absolute value of 3:
[tex]\[ |3| = 3 \][/tex]
Finally, add the results:
[tex]\[ 1.0 + 3 = 4.0 \][/tex]
Therefore, the value of the expression when [tex]\( a = 2 \)[/tex] is:
[tex]\[ \boxed{4.0} \][/tex]
