RootsSquare and cube roots
Name: Date:
Find each root. Check the symbol before you answer.
1289 =
2324 =
3216 =
49 =
5121 =
6125 =
- Free
- Grade 8
- Squares to 625, cubes to 1728
Square roots and cube roots worksheets
A square root asks a question: which number, times itself, gives this one? These free printable worksheets evaluate perfect squares and perfect cubes, so every answer is a whole number.
Kid stuck on one? You don’t just get the sheet.
- Answer key included
- Reopen this exact sheet
- Letter & A4 ready
Ready to printSquare roots and cube roots
The answer key prints on a separate page.
What's on this sheet
The error worth designing against is not arithmetic. Handed √324, a child who has known the symbol for a week divides — 324 ÷ 2 = 162 — because a radical looks like an operator that does something TO the number. Every sheet here is built so the question can be re-read as a question, and the step-by-step walk opens by doing exactly that.
Why this sheet works
The mixed setting is the one worth choosing, and it exists for a single reliable mistake: reading ∛ as √. A page of square roots never tests whether a child checks the symbol, because there is nothing to check. A page that alternates them does, and it is the only page that does.
How this one works
One question from this sheet, worked through a step at a time.
√289
√289=▢
10²=100— under
20²=400— over
√289is between10 and 20
√289=13 or 17
√289=17
17 × 17=289
√289=17
- √ asks a question: which number times itself gives 289? It is not an instruction to halve 289 — that is the mistake this symbol collects.
- Bracket it first. 10² = 100, which is under 289, and 20² = 400, which is over. So the answer is between 10 and 20.
- Now the last digit. 289 ends in 9, and the only digits whose square ends in 9 are 3 and 7. Between 10 and 20 that leaves 13 or 17.
- Two left, and the bracket picks between them: 289 is nearer 400 than 100, so take the bigger one — 17.
- Check it: 17 × 17 = 289. So √289 = 17.