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A square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, written as \( \sqrt{9} = 3 \). This is because \( 3 \times 3 = 9 \).

When you see a square root symbol (\( \sqrt{ } \)), it means you need to find the number which, when squared, gives the value inside the symbol.

Sometimes, the value inside the square root is not a whole number (integer). For instance, \( \sqrt{2} \) is approximately 1.4142 and goes on infinitely without repeating.

For the above exercise, the value inside the square root is a fraction. By following the steps, we simplify by taking the square root of both the numerator and the denominator.

Fractions represent parts of a whole. They consist of a numerator, which is the top number, and a denominator, which is the bottom number. For example, in the fraction \( \frac{1}{2} \), the numerator is 1, and the denominator is 2.

When working with fractions, it's crucial to understand these components. The numerator shows how many parts you have, while the denominator shows the total number of parts the whole is divided into.

In the exercise, the fraction \( \frac{100}{121} \) needs to be simplified by taking the square root of both numbers.

To simplify a square root that involves a fraction, like \( \sqrt{ \frac{100}{121}} \), focus on the numerator and denominator separately.

• First, identify the square root of the numerator: \( \sqrt{100} = 10 \).
• Next, find the square root of the denominator: \( \sqrt{121} = 11 \).

Now, combine these results to form the simplified fraction: \( \frac{10}{11} \).

This approach makes it easier to handle complex expressions by breaking them down into more manageable parts.