A free printable square roots worksheet for Grade 8 math.
By Kris Reddy, Ontario teacher · Updated October 16, 2026 · 26 questions (30 marks) · PDF + answer key
This free square roots worksheet helps Grade 8 students master perfect squares and square roots, and see how the two undo each other. Students square numbers, find square roots of perfect squares and decimals like 1.44, and connect square roots to the side lengths of drawn squares.
They then decide which numbers are perfect squares, estimate square roots between two whole numbers, place square roots on a number line, and solve three real-world problems about a garden, floor tiles and a patio. Every answer in the key shows the working and was checked by computer. To print it, use the Download button above.
| Part | Skill practised | Marks |
|---|---|---|
| A | Square each number | 4 |
| B | Find square roots of perfect squares | 4 |
| C | Squares and area (4 drawn squares) | 4 |
| D | Perfect square or not? | 2 |
| E | Estimate square roots between whole numbers | 4 |
| F | Square roots on a number line | 4 |
| G | Three real-world problems | 6 |
| H | Spot the mistake | 2 |
The square roots worksheet supports the Ontario Grade 8 math curriculum in the Number strand, where students work with perfect squares, square roots and estimation. It's also the ideal warm-up before the Pythagorean theorem worksheet, which uses square roots in every question.
To square a number, multiply it by itself: 6² = 6 × 6 = 36. The answers you get from squaring whole numbers are called perfect squares. Knowing the first fifteen by heart makes every other skill on this square roots worksheet faster.
| n | n² | n | n² |
|---|---|---|---|
| 1 | 1 | 11 | 121 |
| 2 | 4 | 12 | 144 |
| 3 | 9 | 13 | 169 |
| 4 | 16 | 14 | 196 |
| 5 | 25 | 15 | 225 |
A quick test: a perfect square can never end in 2, 3, 7 or 8. So 200 might be one, but you still need to check: 14² = 196 and 15² = 225, so 200 is not a perfect square.
The square root undoes squaring. √36 asks, "what number times itself gives 36?" The answer is 6. That's why square roots and squares are so closely linked to geometry: a square with area A has a side length of √A.
Square roots work for decimals too. Since 1.2 × 1.2 = 1.44, √1.44 = 1.2. Part C of the square roots worksheet has students go both ways, from area to side length and from side length to area. For more background, see square root on Wikipedia.
Most numbers aren't perfect squares, so their square roots are long decimals. To estimate one, find the perfect squares on either side. For √20: 16 < 20 < 25, so √20 is between 4 and 5. Because 20 is closer to 16, √20 is closer to 4 (about 4.5). For √5: 4 < 5 < 9, so √5 is a bit more than 2 (about 2.2).
Students estimate first, then use a calculator to check. This builds number sense instead of button-pressing, which is the real goal of a square roots worksheet at this level.
These questions match the square roots worksheet PDF, which has the squares drawn, answer lines, tables and a number line to mark.
Open each part to check the square roots worksheet answers. The printable key is on the last two pages of the PDF.
These are the errors that come up most when marking this square roots worksheet. Part H targets two of them directly.
For more practice, try the exponent rules worksheet, the scientific notation worksheet and the algebra basics quiz.
Yes. The worksheet and its answer key are free to download and print as one PDF, with no account needed.
A perfect square is a whole number you get by squaring another whole number. 49 is a perfect square because 7 × 7 = 49. 50 is not, because no whole number times itself gives 50.
Find the perfect squares on either side. 36 < 45 < 49, so √45 is between 6 and 7. Since 45 is much closer to 49, √45 is closer to 7. A calculator gives about 6.7.
A square with area A has a side length of √A. A square with area 64 cm² has sides of √64 = 8 cm.
It is written for Grade 8 math and works as review for Grade 9, especially before the Pythagorean theorem.
Ready to start? Use the Download button above to print the free square roots worksheet double-sided, and keep the answer key pages for marking.