Let's solve the given expression step-by-step:
The expression we need to evaluate is:
[tex]\[ 2 \sqrt{144} + (4 + 2 - 6 + 2)^2 - \sqrt{4} + \sqrt{25} \][/tex]
1. Calculate [tex]\(2 \sqrt{144}\)[/tex]:
[tex]\[
\sqrt{144} = 12
\][/tex]
Therefore,
[tex]\[
2 \sqrt{144} = 2 \times 12 = 24
\][/tex]
2. Evaluate the inner expression [tex]\((4 + 2 - 6 + 2)\)[/tex]:
[tex]\[
4 + 2 = 6
\][/tex]
[tex]\[
6 - 6 = 0
\][/tex]
[tex]\[
0 + 2 = 2
\][/tex]
Thus, the value of the inner expression is [tex]\(2\)[/tex].
3. Square the result of the inner expression:
[tex]\[
(2)^2 = 2^2 = 4
\][/tex]
4. Calculate [tex]\(\sqrt{4}\)[/tex]:
[tex]\[
\sqrt{4} = 2
\][/tex]
5. Calculate [tex]\(\sqrt{25}\)[/tex]:
[tex]\[
\sqrt{25} = 5
\][/tex]
6. Combine all the parts:
Now we have all the values we need to substitute back into the original expression:
[tex]\[
2 \sqrt{144} = 24
\][/tex]
[tex]\[
(4 + 2 - 6 + 2)^2 = 4
\][/tex]
[tex]\[
- \sqrt{4} = -2
\][/tex]
[tex]\[
+ \sqrt{25} = 5
\][/tex]
Combining these, we get:
[tex]\[
24 + 4 - 2 + 5
\][/tex]
Step-by-step calculation:
[tex]\[
24 + 4 = 28
\][/tex]
[tex]\[
28 - 2 = 26
\][/tex]
[tex]\[
26 + 5 = 31
\][/tex]
Therefore, the value of the entire expression is:
[tex]\[
\boxed{31}
\][/tex]
