Square Roots Practice
20 questions · 60 seconds · perfect squares from √4 to √225
Free · no login · instant feedback on every answer
Make the perfect squares work backwards: 20 square root questions from √4 to √225, each with an exact whole-number answer, against a 60-second clock. If the squares from 2² to 15² are familiar, this drill turns that knowledge inside out — seeing 144 and instantly knowing 12.
Instant recall of square roots pays off all through middle and high school math: the Pythagorean theorem, simplifying radicals, estimating irrational roots, and solving quadratic equations all start from knowing the perfect squares cold. A student who recognizes 169 as 13² can bracket √170 in a heartbeat; a student who doesn't is stuck computing.
Tips That Make It Stick
- Learn squares and roots as pairs. 12² = 144 and √144 = 12 are the same fact in both directions. Saying each perfect square both ways — "twelve squared is 144, root 144 is twelve" — builds the two-way link this game tests.
- Use the last digit as a filter. Perfect squares can only end in 0, 1, 4, 5, 6, or 9. And the ending narrows the root: a square ending in 6 comes from a root ending in 4 or 6 (196 → 14).
- Anchor on the landmarks. √100 = 10, √144 = 12, and √225 = 15 divide the range into zones. An unfamiliar root like √169 must sit between the landmarks around it.
Frequently Asked Questions
What is a perfect square?
A number that is the product of a whole number with itself: 36 is a perfect square because 6 × 6 = 36. Perfect squares are exactly the numbers whose square roots come out whole, which is why they are the right place to start with radicals.
What grade learns square roots?
Square roots are formally introduced in 8th grade pre-algebra alongside the Pythagorean theorem, though many curricula preview perfect squares in 6th and 7th grade exponent work.
Which square roots should be memorized?
The roots of the perfect squares from 4 through 225 — that is, knowing 2² through 15² in both directions. This set covers nearly every exact root that appears in middle school and Algebra 1 problems.
📝 Matching Printable Worksheets
Prefer paper practice? These free PDF worksheets cover the same skill — each includes an answer key: