Learn about perfect squares and their properties in Alberta Grade 9 Mathematics. Free interactive lesson with examples and practice problems.
Lesson 1.1 of Square Roots & Surface Area in Grade 9 Math — Alberta curriculum lessons.
Now that you know what a perfect square is, let's look at some examples!
When a number is multiplied by itself, the result is a perfect square.
These are the most common ones you'll use in Grade 9 math.
Memorizing the first 20 perfect squares will make math problems much faster — especially when you start working with square roots, algebra, and geometry.
You'll see these numbers again and again in questions like:
"Find √49" "If the area is 81 cm², what's the side length?" "Simplify x² = 64"
💡 Pro Tip. Knowing them by heart will save you time and help you spot patterns instantly.
You already know that a perfect square is made by multiplying a number by itself.
But what happens when that number is negative? 🤔
Let's find out.
When you square a number — whether it's positive or negative — the answer is always positive. ✅
That's because a negative multiplied by a negative equals a positive.
Examples:. (+7) × (+7) = 49; (-7) × (-7) = 49
Both give 49, so 49 is a perfect square of both +7 and -7.
When we write this using exponents:. (+7)² = 49; (-7)² = 49
That means when you square a negative number, the result is the same as squaring its positive version.
💬 In math, we say:. "The square of a negative number is the same as the square of its positive."
⚠️ This is a very common mistake students make:. (-4)² = 16 ✅; -4² = 16 ❌
Why?
Because in -4², the exponent only applies to 4, not to the negative sign. So it becomes -(4 × 4) = -16.
🧩 Tip. Always use parentheses when squaring a negative number: (-4)² = 16
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