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!
Create a free Studyio account to take the full lesson with voice-over teaching, practice questions and instant feedback.