Multiply Square Roots: √(3/2) × √3 × √(9/2) Calculation

Solve the following exercise:

$\sqrt{\frac{3}{2}}\cdot\sqrt{3}\cdot\sqrt{\frac{9}{2}}=$

To solve this problem, we'll follow these steps:

• Identify and combine the square roots into a single square root.
• Simplify the expression logically inside the square root.
• Resolve the final numerical value.

Now, let's work through each step:

Step 1: Convert the expression:

$\sqrt{\frac{3}{2}} \cdot \sqrt{3} \cdot \sqrt{\frac{9}{2}} = \sqrt{\frac{3}{2} \cdot 3 \cdot \frac{9}{2}}$

This results in a single square root.

Step 2: Simplify inside the square root:

$\frac{3}{2} \cdot 3 \cdot \frac{9}{2} = \frac{3 \cdot 3 \cdot 9}{2 \cdot 2} = \frac{81}{4}$

Step 3: Calculate the square root:

• The square root of $\frac{81}{4}$ can be found by separately taking square roots of the numerator and the denominator:
• $\sqrt{\frac{81}{4}} = \frac{\sqrt{81}}{\sqrt{4}} = \frac{9}{2}$

Thus, combining all parts logically, we resolve the expression:

$\frac{9}{2} = 4\frac{1}{2}$

Therefore, the solution to the problem is $\boxed{4\frac{1}{2}}$.