Squares & Cubes Worksheet

There are five sets of exponents worksheets:

• Squares & cubes
  
• Whole number exponents
  
• Negative whole number exponents
  
• Unit fraction exponents (positive or negative)
  
• Fractional exponents (positive or negative)

Examples, solutions, videos, and worksheets to help Grade 6 students learn how to calculate squares and cubes of a number. The number, also called the base, can be a positive or negative whole number, a positive or negative fraction, a positive or negative decimal.

How to calculate squares and cubes of a number?

There are four sets of squares and cubes worksheets:

• Positive Whole Number Base
• Negative Whole Number Base
• Fractional Base (Positive or Negative)
• Decimal Base (Positive or Negative)

Exponents, also known as powers or indices, are mathematical expressions that represent repeated multiplication of a base number by itself. They are a shorthand way of writing large or small numbers.

In an exponent expression, the base number is raised to a certain power, which is indicated by a superscript or a raised number to the right of the base. The power represents the number of times the base is multiplied by itself.

For example, in the expression 2³, the base is 2, and the power is 3. This means that 2 is multiplied by itself three times: 2 × 2 × 2 = 8. So, 2³ equals 8.

 

Squares and cubes are special cases of exponents where the power is specifically 2 or 3, respectively.

Squares: When a number is raised to the power of 2, it is called a square. Squaring a number means multiplying it by itself. For example, 3 squared (written as 3²) is 3 × 3 = 9. Similarly, (-2)² is (-2) × (-2) = 4.

Squares have these properties:

• The square of a positive number is always positive.
• The square of a negative number is always positive.
• The square of 0 is 0.
• The square of a number greater than 1 is greater than the original number, while the square of a number between 0 and 1 is smaller than the original number.

Cubes: When a number is raised to the power of 3, it is called a cube. Cubing a number means multiplying it by itself twice. For example, 2 cubed (written as 2³) is 2 × 2 × 2 = 8. Similarly, (-3)³ is (-3) × (-3) × (-3) = -27.

Cubes have these properties:

• The cube of a positive number remains positive.
• The cube of a negative number remains negative.
• The cube of 0 is 0.
• The cube of a number greater than 1 is greater than the original number, while the cube of a number between 0 and 1 is smaller than the original number.

Have a look at this video if you need to review how to calculate squares and cubes.

• Squaring and Cubing Numbers

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Squares & Cubes Worksheets.

 

More Squares & Cubes Worksheets

Printable
(Answers on the second page.)
Squares & Cubes Worksheet #1 (Positive Whole Number Bases)
Squares & Cubes Worksheet #2 (Negative Whole Number Bases)
Squares & Cubes Worksheet #3 (Positive or Negative Fractional Bases)
Squares & Cubes Worksheet #4 (Positive or Negative Decimal Bases)

Generated
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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