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Simplify [tex]7 + \sqrt{6(3+4) - 2 + 9} - 3 \cdot 2^2[/tex].

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GinnyAnsweridn
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]
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