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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