Square Roots and Perfect Squares

Introduction

In this lesson, we will explore square roots and perfect squares. A perfect square is a number that can be expressed as the square of an integer. For example, $1, 4, 9, 16,$ and $25$ are perfect squares because they are $1^{2}$, $2^{2}$, $3^{2}$, $4^{2}$, and $5^{2}$ respectively.

Square Roots

The square root of a number $x$ is a value $y$ such that $y^{2} = x$. We denote the square root of $x$ as $\sqrt{x}$. For example, the square root of $16$ is $4$ because $4^{2} = 16$. This can be written as:

$$\sqrt{16} = 4$$

Example

Let's find the square roots of the perfect square $36$:

1. Identify that $36$ is a perfect square because it equals $6^{2}$.
2. The square root of $36$ is:

$$\sqrt{36} = 6$$

3. The negative square root is also valid:

$$\sqrt{36} = -6 \text{ (since } (-6)^{2} = 36)$$

Key Questions

• What are perfect squares up to $100$?
• How do you find the square root of a number?
• Can a number have more than one square root? If so, how?

Conclusion

Understanding square roots and perfect squares is essential in mathematics, as it forms the basis for more advanced concepts in algebra and geometry.