Master square roots of perfect squares in Alberta Grade 9. Step-by-step guide with interactive examples and quizzes.
Lesson 1.2 of Square Roots & Surface Area in Grade 9 Math: Alberta curriculum lessons.
You've already seen how to find square roots of whole numbers and fractions, but did you know some decimals can also be perfect squares?
Let's explore how that works.
Key Concept. A decimal is a perfect square if it can be written as a fraction that is a perfect square.
For example:
Both 36 and 100 are perfect squares: √36 = 6 and √100 = 10 ✅ That means 0.36 is a perfect square because its square root is a clean decimal (0.6).
The same rule you learned for fractions works here too:
If the decimal can be turned into that kind of fraction, and both parts are perfect squares. You'll get a nice, clean result.
So far, you've worked with whole numbers, but fractions can be perfect squares too!
Let's explore how that works.
Key Concept. A fraction is a perfect square if both the numerator and denominator are perfect squares.
That means each part, top and bottom, can be square-rooted evenly.
Step-by-Step Process. Follow these steps to check if a fraction is a perfect square:
This only gives a simple fraction when both a and b are perfect squares.
Summary. Remember these key relationships:
Imagine a square divided into equal parts. That's your fraction.If both the shaded area (numerator) and the total area (denominator) form squares, then the whole fraction is a perfect square.
Understanding the Pattern. Notice how both the shaded area (4 squares in a 2×2 pattern) and the total area (9 squares in a 3×3 grid) form perfect squares!
Problem. You're designing a small square tile with an area of 0.49 m². To find the length of each side:
Each side of the tile is 0.7 meters long.
That's how you can work with square roots of decimals in real measurements!
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