Absolutely! Let's break down the expression step-by-step to simplify it. The expression we need to simplify is:
[tex]\[7 + \sqrt{6(3+4) - 2 + 9} - 3 \cdot 2^2\][/tex]
1. Simplify within the parentheses:
[tex]\[3 + 4 = 7\][/tex]
This gives us:
[tex]\[7 + \sqrt{6(7) - 2 + 9} - 3 \cdot 2^2\][/tex]
2. Multiply within the expression inside the square root:
[tex]\[6 \cdot 7 = 42\][/tex]
Now the expression is:
[tex]\[7 + \sqrt{42 - 2 + 9} - 3 \cdot 2^2\][/tex]
3. Perform the remaining arithmetic inside the square root:
[tex]\[42 - 2 = 40\][/tex]
[tex]\[40 + 9 = 49\][/tex]
So the expression now simplifies to:
[tex]\[7 + \sqrt{49} - 3 \cdot 2^2\][/tex]
4. Evaluate the square root:
[tex]\[\sqrt{49} = 7\][/tex]
Now the expression is:
[tex]\[7 + 7 - 3 \cdot 2^2\][/tex]
5. Evaluate the exponentiation:
[tex]\[2^2 = 4\][/tex]
So we have:
[tex]\[7 + 7 - 3 \cdot 4\][/tex]
6. Perform the multiplication:
[tex]\[3 \cdot 4 = 12\][/tex]
This makes the expression:
[tex]\[7 + 7 - 12\][/tex]
7. Add and subtract to simplify the final expression:
[tex]\[7 + 7 = 14\][/tex]
[tex]\[14 - 12 = 2\][/tex]
So, after simplifying the expression step-by-step, the final result is:
[tex]\[2\][/tex]
