Evaluating the Expression Step-by-Step

The problem requires calculating the value of the expression:

$ \frac{\sqrt{225}}{14} \times \frac{\sqrt{196}}{22} \times \frac{\sqrt{484}}{15} $

First, find the square roots of the numbers in the numerators:

• $ \sqrt{225} = 15 $
• $ \sqrt{196} = 14 $
• $ \sqrt{484} = 22 $

Simplifying the Expression

Substitute these values back into the original expression:

$ \frac{15}{14} \times \frac{14}{22} \times \frac{22}{15} $

Performing Multiplication and Cancellation

Now, multiply the fractions. Notice that several terms cancel each other out:

$ \frac{15 \times 14 \times 22}{14 \times 22 \times 15} $

The expression simplifies due to cancellation:

$ \left( \frac{15}{15} \right) \times \left( \frac{14}{14} \right) \times \left( \frac{22}{22} \right) $

This equals:

$ 1 \times 1 \times 1 = 1 $

Therefore, the value of the expression is 1.