Certainly! Let's solve the expression step-by-step:
Given expression:
[tex]\[ 2 - 4 + 3 \left( \sqrt{5} \times 12 \div \left(2 + \frac{2^3}{2}\right) - 1 \right) \][/tex]
1. Calculate the exponentiation and division inside the parentheses:
[tex]\[ 2^3 = 8 \][/tex]
[tex]\[ \frac{8}{2} = 4 \][/tex]
2. Add this result to the number outside the inner parentheses:
[tex]\[ 2 + 4 = 6 \][/tex]
3. Now we proceed with the multiplication, division and the nested expression inside the parentheses:
[tex]\[ \sqrt{5} \][/tex]
The square root of 5 is approximately:
[tex]\[ \sqrt{5} \approx 2.23606797749979 \][/tex]
4. Continue with the multiplication and division:
[tex]\[ \sqrt{5} \times 12 \approx 2.23606797749979 \times 12 = 26.83281572999748 \][/tex]
[tex]\[ 26.83281572999748 \div 6 = 4.47213595499958 \][/tex]
5. Subtract 1 from the obtained result:
[tex]\[ 4.47213595499958 - 1 = 3.4721359549995796 \][/tex]
6. Multiply by 3:
[tex]\[ 3 \times 3.4721359549995796 = 10.416407864998739 \][/tex]
7. Now incorporate this result into the original expression:
[tex]\[ 2 - 4 + 10.416407864998739 \][/tex]
[tex]\[ 2 - 4 = -2 \][/tex]
8. Finally, add the last two parts:
[tex]\[ -2 + 10.416407864998739 = 8.416407864998739 \][/tex]
Therefore, the value of the expression is:
[tex]\[ 8.416407864998739 \][/tex]
