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Square Numbers Worksheets

This page makes free printable square numbers worksheets on demand: press the button and you get a new sheet of 20 problems with a matching answer key, ready for US Letter or A4 paper. The current sheet starts with problems like √81 and 4², and the answers (9 and 16) are printed on the key so marking takes about a minute.

📄 SQUARE NUMBERS WORKSHEETS — A NEW SHEET EVERY TIME YOU PRESS THE BUTTON
🎲 New set of problems

‘New set of problems’ opens the generator in its own tab. There you can change the problem count and turn the answer key on or off. ‘Print or save as PDF’ opens the print dialog — choose Save as PDF in the printer list to keep the file. The sheet fits US Letter and A4, and the answer key prints on its own page.

What the sheet contains

Knowing the squares up to about fifteen by heart pays for itself repeatedly in later work with area, right-angled triangles and quadratics.

Square roots are included because they are exponents read backwards, and practising both directions together makes each of them faster.

Because each sheet regenerates, the base and the power vary rather than settling into the familiar small cases.

An exponent is repeated multiplication written short. Reading √81 as a multiplication rather than as a symbol is what makes 9 obvious instead of mysterious.

Teachers usually place square numbers worksheets alongside the expressions and equations strand for grade 6, which is where the skill sits in the majority of US state frameworks.

Six problems from the sheet in front of you

These six come from the sheet loaded on this page. Press the button and the numbers change, but the shape stays the same (squares up to 15 × 15).
#ProblemAnswerWhat to check
1√81 =9Watch for: writing the exponent full size
24² =16Check: getting the root of a non-square wrong
3√16 =4Look at: mishandling a power of one
48² =64Ask about: confusing the square with double
513² =169Watch for: losing track of the base in a chain
66² =36Check: multiplying the base by the exponent

Try one together first

Take the first problem on the sheet as it stands, √81. Work √81 out on paper rather than in your head the first few times, say each step aloud, and check the result against 9 on the key before moving on.

Here is one worked through. 4² gives 16. If your child arrives somewhere other than 16 on 4², look at the working rather than the answer: nearly every wrong result comes from a skipped step, not an unknown fact.

Three mistakes we see most often

Getting the most out of 10 minutes a day

  1. Mark it together straight away while the working is still fresh, so a slip like the one behind √16 can be talked through instead of guessed at.
  2. Run the sheet at the same time each day. Ten focused minutes before dinner beats an hour on Sunday, because square numbers and square roots is a recall skill: √81 has to arrive without being worked out, and recall is built by frequency.
  3. Keep the session to about 10 minutes. A child working at this level who is still counting on fingers will need longer than that on a line like √81, and that is fine: the timer is a measurement, never a punishment.
  4. If two days in a row come out under 10 minutes with everything correct, that is the signal to move up: either numbers bigger than √81 uses, or the next skill in the sequence.
  5. Re-print the same skill rather than the same sheet. Because the numbers change, a child who memorised that √81 gives 9 still has to actually calculate tomorrow.

Marking the sheet

The answer key is generated with the worksheet, not written by hand, so it always matches the sheet in front of you — √81 is listed as 9, 4² as 16, and so on down the page.

The key prints on its own page by default. Uncheck the answer-key box before printing if you would rather keep it back and mark the sheet yourself.

Printing and saving as PDF

For a class set, print one sheet, press the new-worksheet button and print again. Each child gets different numbers on the same skill, so nobody can copy the answer to √81 from a neighbour.

If the problems look cramped, drop the count from 20 to a smaller number before printing these square numbers worksheets; the font stays the same size and the spacing opens up.

Frequently asked questions

Is the answer key included?
Yes, on its own page behind the worksheet. For the sheet loaded right now it shows 9 for √81 and 16 for 4².
Why learn the squares by heart?
Because they turn up constantly in area, in right-angled triangles and in quadratics. Knowing them saves seconds on every problem that contains one.
Will these print correctly on A4?
Yes. These square numbers worksheets fit both A4 and US Letter without clipping, as long as print scaling is left at 100% and browser headers and footers are switched off.
Are square roots the opposite of squaring?
Yes, for positive numbers, which is all that appears at this level. Practising both directions together makes each of them faster.

Print a sheet of square numbers worksheets, run it for 10 minutes, mark it together, and come back tomorrow for a different set of numbers on the same skill.

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Free printable math worksheets from a working math academy director in Korea. Problems come from our own code, not from a published workbook. Every sheet prints on US Letter or A4 with its answer key. All worksheets · Worksheet generator · Korean site
Last updated: 2026-09-13