Squares and Square Root Worksheet

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Examples, solutions, videos, and worksheets to help Grade 6 and Grade 7 students learn how to find squares and square roots.

How to evaluate squares and square roots?

Squares and square roots are two closely related concepts in mathematics. A square is a number that is multiplied by itself, and a square root is a number that, when multiplied by itself, equals the original number. For example, 4 is a square because it is equal to 2 multiplied by itself (2 × 2 = 4). The square root of 4 is 2, because 2 × 2 = 4.

We can denote the square of a number using exponents. For example, 3 × 3 = 32 = 9.

The square root is denoted by the symbol “√”. For example, the square root of 9 is written as √9. It’s important to note that the square root can have both positive and negative values. For example, the square root of 9 is both 3 and -3, because 3 × 3 = 9 and -3 × -3 = 9. The square root that is positive is called the principal square root. However, in most cases, when we refer to the square root, we are referring to the principal square root, which is the positive value.

Perfect squares are numbers that can be expressed as the square of an integer. It is obtained by multiplying an integer by itself. For example, 16 is a perfect square because it can be expressed as 4 × 4 = 16. This also means that that the square roots of perfect squares are integers.

Other examples of squares and square roots:

Squares and Square Roots

Have a look at this video if you need to review how to evaluate perfect squares and square roots.

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Squares and Square Root

More Squares and Square Root Worksheets

(Answers on the second page.)
Squares and Square Root Worksheet

Squares with bases 0 to 10
Squares with bases 2 to 20
Squares with bases -10 to 0
Squares with bases -20 to 0

Cubes with bases 0 to 10
Cubes with bases 2 to 20
Cubes with bases -10 to 0
Cubes with bases -20 to 0


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