https://file.aiquickdraw.com/mathbot/file/17261604054944jrsp3pz.jpg

Let's solve each of the given problems step-by-step:

### Problem a:
\[
\sqrt{432} \cdot (\sqrt{726} - \sqrt{486} + \sqrt{294} - \sqrt{600}) + 12\sqrt{2}
\]

### Problem b:
\[
\sqrt{162} \cdot (\sqrt{75} - \sqrt{147} + \sqrt{48} - \sqrt{300}) + 12\sqrt{24}
\]

### Problem c:
\[
\sqrt{24} \cdot [\sqrt{150} - \sqrt{18} - 5(\sqrt{75} - \sqrt{48})]
\]

### Problem d:
\[
\sqrt{54} \cdot (\sqrt{216} - \sqrt{27} - \sqrt{72} - \sqrt{50})
\]

### Problem e:
\[
\sqrt{162} \cdot (\sqrt{90} - \sqrt{360} - 1.5\sqrt{20}) - (\sqrt{18} - \sqrt{32})
\]

To find the solutions, we will first simplify each square root term and then perform the arithmetic operations. Let's start with solving problem (a) and proceed with the others sequentially.The simplified expression for problem (a) is:

\[
\sqrt{432} \cdot (\sqrt{726} - \sqrt{486} + \sqrt{294} - \sqrt{600}) + 12\sqrt{2} = -24\sqrt{2}
\]

Evaluating this gives approximately:

\[
-24\sqrt{2} \approx -33.94
\]

Next, let's proceed with solving problem (b).It seems like I can’t do more advanced data analysis right now. Please try again later. 

If you would like, I can guide you through solving problem (b) manually or help you with any other math-related questions. Let me know how you would like to proceed!

Solve the following expressions involving square roots and arithmetic operations:
a) √432 · (√726 - √486 + √294 - √600) + 12√2
b) √162 · (√75 - √147 + √48 - √300) + 12√24
c) √24 · [√150 - √18 - 5(√75 - √48)]
d) √54 · (√216 - √27 - √72 - √50)
e) √162 · (√90 - √360 - 1.5√20) - (√18 - √32)

Learn how to solve complex expressions involving square roots, simplifications, and arithmetic operations. Step-by-step guidance for problems like √432 · (√726 - √486 + √294 - √600) + 12√2. Suitable for high school students, Grades 9-12.

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