Understanding Square Roots

What is a Square Root?

A square root of a number is a value that, when multiplied by itself, gives the number. In mathematical terms, for a non-negative real number \( x \), the square root of \( x \) is a number \( y \) such that \( y^2 = x \).

Formula

The square root is denoted by the radical symbol \( \sqrt{} \). The formula is:

\[ y = \sqrt{x} \]

Where:

• \( x \) is the number we're finding the square root of
• \( y \) is the square root of \( x \)

Calculation Steps

Let's calculate the square root of 25:

1. Identify the number: \( x = 25 \)
2. Apply the square root formula: \( y = \sqrt{25} \)
3. Calculate: \( y = 5 \) (because \( 5 \times 5 = 25 \))
4. Verify: \( 5^2 = 25 \)

Example and Visual Representation

Let's visualize the square root of 25:

This square visually represents:

• The side length of the square is 5 units
• The area of the square is 25 square units
• Therefore, the square root of 25 is 5