To solve this problem, follow these step-by-step instructions:
1. Identify and calculate \( p \):
The problem states that \( p = 2x \). Given \( x = 3 \),
[tex]\[
p = 2 \cdot 3 = 6
\][/tex]
2. Identify and calculate \( q \):
The problem states that \( q = 3x \). Given \( x = 3 \),
[tex]\[
q = 3 \cdot 3 = 9
\][/tex]
3. Calculate the product \( 6pq \):
We now know \( p = 6 \) and \( q = 9 \). Therefore,
[tex]\[
6pq = 6 \cdot 6 \cdot 9
\][/tex]
Calculate this step-by-step:
[tex]\[
6 \cdot 6 = 36
\][/tex]
[tex]\[
36 \cdot 9 = 324
\][/tex]
4. Find the square root of \( 6pq \):
We have \( 6pq = 324 \). Now, we need to find the square root of 324:
[tex]\[
\sqrt{324} = 18
\][/tex]
So, the value of \( \sqrt{6pq} \) is 18.
Thus, the values are:
[tex]\[
p = 6, \quad q = 9, \quad \sqrt{6pq} = 18.0
\][/tex]
