Certainly! Let's break down the problem step by step:
We start with the expression:
[tex]\[
\sqrt{25+24} + \left[ \left(5^3 - 100\right) + \left(\sqrt{25} + \sqrt{822}\right) + 5 \right]
\][/tex]
### Step 1: Simplify the Square Root Expression
First, simplify [tex]\(\sqrt{25 + 24}\)[/tex]:
[tex]\[
25 + 24 = 49
\][/tex]
[tex]\[
\sqrt{49} = 7
\][/tex]
So, [tex]\(\sqrt{25+24} = 7\)[/tex].
### Step 2: Simplify Inside the Brackets
Next, simplify the expression inside the brackets, starting with:
[tex]\[
5^3 - 100
\][/tex]
Calculate [tex]\(5^3\)[/tex]:
[tex]\[
5^3 = 125
\][/tex]
Then, subtract 100:
[tex]\[
125 - 100 = 25
\][/tex]
We continue by simplifying [tex]\(\sqrt{25}\)[/tex] and [tex]\(\sqrt{822}\)[/tex]:
[tex]\[
\sqrt{25} = 5
\][/tex]
We represent [tex]\(\sqrt{822}\)[/tex] as an approximate value:
[tex]\[
\sqrt{822} \approx 28.67
\][/tex]
So the expression inside the brackets becomes:
[tex]\[
(25) + (5) + (28.67) + 5
\][/tex]
### Step 3: Sum Inside the Brackets
Let's add everything inside the brackets:
[tex]\[
25 + 5 + 28.67 + 5 = 63.67
\][/tex]
### Step 4: Combine Results
Finally, add the results from outside and inside the brackets:
[tex]\[
7 + 63.67 = 70.67
\][/tex]
### Conclusion
The final result of the expression is:
[tex]\[
70.67
\][/tex]
