What is a Perfect Square? Meaning and Examples in Algebra 1

📚 Quick Study Guide

🔢 Definition: A perfect square is a number that can be obtained by squaring an integer. In other words, it's the result of multiplying an integer by itself. ➕ Formula: If $n$ is an integer, then $n^2$ is a perfect square. 💡 Examples:
• 1 ($1^2 = 1$)
• 4 ($2^2 = 4$)
• 9 ($3^2 = 9$)
• 16 ($4^2 = 16$)
• 25 ($5^2 = 25$)
🧮 Algebraic Perfect Squares: These often appear in factoring and solving quadratic equations. Examples include $(x+a)^2 = x^2 + 2ax + a^2$. 📐 Recognizing Perfect Square Trinomials: A trinomial in the form $ax^2 + bx + c$ is a perfect square if it can be written as $(px + q)^2$ or $(px - q)^2$.

🤔 Practice Quiz

1. Which of the following numbers is a perfect square?
   1. 3
   2. 8
   3. 16
   4. 27
2. Which of the following expressions is a perfect square trinomial?
   1. $x^2 + 4x + 5$
   2. $x^2 + 6x + 9$
   3. $x^2 + 2x + 3$
   4. $x^2 + 8x + 15$
3. What is the square root of 49?
   1. 6
   2. 7
   3. 8
   4. 9
4. Which of the following is NOT a perfect square?
   1. 1
   2. 9
   3. 15
   4. 100
5. Factor the perfect square trinomial: $x^2 + 10x + 25$
   1. $(x + 3)^2$
   2. $(x + 4)^2$
   3. $(x + 5)^2$
   4. $(x + 6)^2$
6. What is the value of 'c' that makes the expression $x^2 + 12x + c$ a perfect square trinomial?
   1. 6
   2. 12
   3. 24
   4. 36
7. Simplify $\sqrt{64x^2}$:
   1. $4x$
   2. $8x$
   3. $16x$
   4. $32x$