`{:("Quantity A","Quantity B"),(sqrt(30)xxsqrt5,12):}`

Answer

To solve the problem comparing Quantity A and Quantity B, we will follow these steps:

### Step 1: Identify the quantities
- Quantity A = \( \sqrt{30} \times \sqrt{5} \)
- Quantity B = 12

### Step 2: Simplify Quantity A
We can simplify Quantity A using the property of square roots:
\[ \sqrt{30} \times \sqrt{5} = \sqrt{30 \times 5} \]
Calculating \( 30 \times 5 \):
\[ 30 \times 5 = 150 \]
Thus, Quantity A becomes:
\[ \sqrt{150} \]

### Step 3: Further simplify \( \sqrt{150} \)
We can factor 150 to simplify it further:
\[ 150 = 25 \times 6 = 5^2 \times 6 \]
Using the property of square roots:
\[ \sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5 \sqrt{6} \]

### Step 4: Approximate \( \sqrt{6} \)
Now we need to approximate \( \sqrt{6} \). The approximate value of \( \sqrt{6} \) is about 2.449.
Thus:
\[ 5 \sqrt{6} \approx 5 \times 2.449 = 12.245 \]

### Step 5: Compare Quantity A and Quantity B
Now we compare:
- Quantity A \( \approx 12.245 \)
- Quantity B = 12

Since \( 12.245 > 12 \), we conclude that:
\[ \text{Quantity A is greater than Quantity B.} \]

### Final Conclusion
Thus, the final answer is that Quantity A is greater than Quantity B.

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