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Simplifying fractions is a fundamental skill in algebra. It involves reducing a fraction to its simplest form by ensuring the numerator and the denominator have no common factors other than 1. The same principle applies when dealing with square roots of fractions.
When you encounter a fraction under a square root, you can simplify your work by treating the numerator and the denominator separately. If both parts are perfect squares, you can easily take the square root of each part.
For example, in our exercise, we have \(\frac{225}{169}\) under the square root. Here, both 225 and 169 are perfect squares. So, you can simplify by taking the square root of each part separately, eventually leading you to \(\frac{15}{13}\).

Understanding the roles of numerators and denominators in fractions is essential.
The numerator is the top number in a fraction and represents how many parts we have. In our exercise, the numerator is 225.
The denominator is the bottom number and tells us into how many parts the whole is divided. In our exercise, the denominator is 169.
When simplifying fractions, you focus on these two numbers. If both the numerator and the denominator are perfect squares, like in this instance, you can take the square root of each separately. This step simplifies our calculation tremendously.

Perfect squares are numbers that are the square of an integer. Recognizing perfect squares is crucial when solving problems involving square roots.
Some common perfect squares include:

• 1 (since 1x1=1)
• 4 (since 2x2=4)
• 9 (since 3x3=9)
• 16 (since 4x4=16)
• 25 (since 5x5=25)
• 36 (since 6x6=36)

In our exercise, both 225 and 169 are perfect squares. Knowing this, you can directly find their square roots. The square root of 225 is 15 and the square root of 169 is 13.
This understanding helps you quickly simplify \(\frac{225}{169}\) to \( \frac{15}{13}\). Recognizing and working with perfect squares simplifies many mathematical problems significantly.