Square Roots Test
mediumThis test asks for the square roots of perfect squares, such as √144 = 12. Easy goes up to √225, Medium covers √121 to √900, and Hard stretches to √2500.
Square roots from √121 to √900.
Every question has a whole-number answer, so there are no decimals to worry about. Use the chart to check yourself, and the last-digit trick below to narrow the answer down in seconds.
Perfect squares and their square roots (1 to 50)
| Perfect square | Square root | Perfect square | Square root |
|---|---|---|---|
| 1 | √1 = 1 | 676 | √676 = 26 |
| 4 | √4 = 2 | 729 | √729 = 27 |
| 9 | √9 = 3 | 784 | √784 = 28 |
| 16 | √16 = 4 | 841 | √841 = 29 |
| 25 | √25 = 5 | 900 | √900 = 30 |
| 36 | √36 = 6 | 961 | √961 = 31 |
| 49 | √49 = 7 | 1024 | √1024 = 32 |
| 64 | √64 = 8 | 1089 | √1089 = 33 |
| 81 | √81 = 9 | 1156 | √1156 = 34 |
| 100 | √100 = 10 | 1225 | √1225 = 35 |
| 121 | √121 = 11 | 1296 | √1296 = 36 |
| 144 | √144 = 12 | 1369 | √1369 = 37 |
| 169 | √169 = 13 | 1444 | √1444 = 38 |
| 196 | √196 = 14 | 1521 | √1521 = 39 |
| 225 | √225 = 15 | 1600 | √1600 = 40 |
| 256 | √256 = 16 | 1681 | √1681 = 41 |
| 289 | √289 = 17 | 1764 | √1764 = 42 |
| 324 | √324 = 18 | 1849 | √1849 = 43 |
| 361 | √361 = 19 | 1936 | √1936 = 44 |
| 400 | √400 = 20 | 2025 | √2025 = 45 |
| 441 | √441 = 21 | 2116 | √2116 = 46 |
| 484 | √484 = 22 | 2209 | √2209 = 47 |
| 529 | √529 = 23 | 2304 | √2304 = 48 |
| 576 | √576 = 24 | 2401 | √2401 = 49 |
| 625 | √625 = 25 | 2500 | √2500 = 50 |
How to find square roots quickly
- Learn the squares first, then run them backwards. If you know 13² = 169, you know √169 = 13.
- Look at the last digit. A perfect square ending in 1 has a root ending in 1 or 9; ending in 4: 2 or 8; ending in 5: 5; ending in 6: 4 or 6; ending in 9: 3 or 7; ending in 0: 0.
- Bracket it between round squares. For √529: 20² = 400 and 30² = 900, so the root is in the 20s. It ends in 9, so the units digit is 3 or 7. Since 25² = 625 is bigger than 529, the answer is 23.
- Another example, √1764: 40² = 1600 and 50² = 2500, so it is in the 40s. It ends in 4, so the units digit is 2 or 8. Since 45² = 2025 is bigger than 1764, the answer is 42.
- Prime factors also work: 1296 = 2⁴ × 3⁴, so √1296 = 2² × 3² = 4 × 9 = 36.
Frequently asked questions
What is the square root of 144?
√144 = 12, because 12 × 12 = 144.
What is the square root of 2025?
√2025 = 45, because 45 × 45 = 2025.
How do you find the square root of a perfect square without a calculator?
Bracket it between round squares. For √529: 20² = 400 and 30² = 900, so the root is in the 20s. It ends in 9, so the units digit is 3 or 7. Since 25² = 625 is bigger than 529, the answer is 23.
What if a number is not a perfect square?
Its root is not a whole number. For example √50 is about 7.07. This test only uses perfect squares, so every answer is a whole number.
How is the speed maths test scored?
Each test has 10 questions. Answer 8 or more correctly to pass. Your time is recorded for the whole test, and your best time for each test and level is saved on your own device, so you can try to beat it.