Learn to calculate and approximate square roots of non-perfect squares. Alberta Grade 9 math curriculum with practice exercises.
Lesson 1.3 of Square Roots & Surface Area in Grade 9 Math — Alberta curriculum lessons.
You already know that perfect squares are numbers made by multiplying a whole number by itself:
3 × 3 = 9, 5 × 5 = 25, 8 × 8 = 64
Their square roots are always whole numbers:
√9 = 3, √25 = 5, √64 = 8
But what about numbers that aren't made this way?That's where non-perfect squares come in. 👇
Definition. A non-perfect square is a number that cannot be written as a product of two equal factors. As a result, their square roots are irrational numbers — decimals that go on forever without repeating.
Here's the key difference between perfect and non-perfect squares:
To estimate the square root of a whole number, find the two perfect squares it falls between.
💡 Universal Rule. This works for every non-perfect square.
To estimate the square root of a decimal number, find the two perfect squares it falls between.
💡 Key Pattern. The same method works for any number with decimals!
To estimate the square root of a fraction, find the perfect squares closest to the numerator and denominator, then find the square root of each.
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