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Printable Square Roots and Cube Roots Worksheet in PDF: Reference Table and Examples

This free printable worksheet gives grade 7 and grade 8 students practice finding square roots and cube roots of both basic and larger numbers. The worksheet includes an answer key, so students can check their own results.

Problems focus on perfect squares and perfect cubes, building the number sense students need before moving into exponents and more advanced algebra. For more practice, explore Brighterly’s exponents worksheets hub.

Square Roots and Cube Roots Worksheet: Free Download

This topic is available as four downloadable worksheet files:

Perfect Squares and Perfect Cubes Reference Table

Before solving square root and cube root problems, it helps to have the first several perfect squares and perfect cubes memorized. Use this table as a quick reference while working through the worksheet:

Number (n)	Square (n²)	Cube (n³)
1	1	1
2	4	8
3	9	27
4	16	64
5	25	125
6	36	216
7	49	343
8	64	512
9	81	729
10	100	1000
11	121	1331
12	144	1728

Worked Example: Finding a Square Root

To find a square root, ask: what number multiplied by itself gives this value?

Worked Example: √144

• Find a number that, multiplied by itself, equals 144.
• From the reference table, 12 × 12 = 144.

√144 = 12

Worked Example: Finding a Cube Root

To find a cube root, ask: what number multiplied by itself three times gives this value?

Worked Example: ∛64

• Find a number that, multiplied by itself three times, equals 64.
• From the reference table, 4 × 4 × 4 = 64.

∛64 = 4

64 is a handy number to know well, since it’s both a perfect square (8²) and a perfect cube (4³).

Quick Answer Check for the Square Roots Section

• √144 = 12
• √81 = 9
• √9 = 3
• √49 = 7
• √100 = 10
• √36 = 6
• √64 = 8
• √16 = 4
• √121 = 11
• √25 = 5

More Roots and Exponents Worksheets

Once your child is confident with square roots and cube roots, explore more of Brighterly’s numbers and exponents practice:

• Square Root Worksheets
• Cube Roots Worksheets
• Exponents Worksheets
• Rule of Exponents Worksheets
• Properties of Exponents Worksheets
• 7th Grade Integers Worksheets
• Scientific Notation Worksheets

What Students Practice With This Square Roots and Cube Roots Worksheet

• Finding square roots of perfect squares
• Finding cube roots of perfect cubes
• Using a reference table to recognize perfect squares and cubes quickly
• Building the number sense needed for exponents and algebra
• Checking work against an included answer key

Each worksheet includes an answer key, so students can check their own results without waiting for a teacher to grade the page. Working from a reference table alongside worked examples gives students a quick way to check whether a number is a perfect square or perfect cube before they start solving.

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Square Roots and Cube Roots Worksheets: FAQ

What is a square root?

A square root of a number is the value that, when multiplied by itself, gives that number. For example, the square root of 144 is 12, because 12 × 12 = 144. Square roots are written with the radical symbol √, and numbers like 144 that have a whole-number square root are called perfect squares.

What is a cube root?

A cube root of a number is the value that, when multiplied by itself three times, gives that number. For example, the cube root of 64 is 4, because 4 × 4 × 4 = 64. Cube roots are written with the radical symbol ∛, and numbers like 64 that have a whole-number cube root are called perfect cubes.

What grade level is this square roots and cube roots worksheet for?

This worksheet is designed for grade 7 and grade 8 students who are building the number sense needed for exponents and algebra. Problems start with basic perfect squares and cubes before moving to larger numbers, matching the level where students first study roots in middle school math class and prepare for high school algebra.

Does this worksheet include an answer key?

Yes, this square roots and cube roots worksheet includes an answer key. Students can check their own results as soon as they finish a problem, which helps them catch mistakes right away, such as confusing a square root with a cube root, instead of waiting for a teacher to grade the assignment.

Is this worksheet free and printable?

Yes, this worksheet is free to download as a printable PDF, and no account or sign-up is required. Students can print the pages for hands-on practice with a pencil and paper, or work through the problems digitally if a printer isn’t available, since the questions work equally well either way.