Name Date
Square roots worksheets
Work out each square root.
1.
√196 =
2.
√289 =
3.
√64 =
4.
√49 =
5.
√16 =
6.
√121 =
7.
√9 =
8.
√256 =
9.
√400 =
10.
√144 =
11.
√100 =
12.
√169 =
13.
√324 =
14.
√4 =
15.
√81 =
16.
√36 =
17.
√225 =
18.
√361 =
Square roots worksheets
Square roots of perfect squares, so every answer is a whole number, with squares on the same page when you want both directions.
Grade 6–Grade 9 · every refresh draws a new set · answer key included
Square roots worksheets — answer key
Work out each square root.
1.
√196 =14
2.
√289 =17
3.
√64 =8
4.
√49 =7
5.
√16 =4
6.
√121 =11
7.
√9 =3
8.
√256 =16
9.
√400 =20
10.
√144 =12
11.
√100 =10
12.
√169 =13
13.
√324 =18
14.
√4 =2
15.
√81 =9
16.
√36 =6
17.
√225 =15
18.
√361 =19
18 problems · US Letter · answer key — 2 sheets, page breaks marked in the preview
What this worksheet is for
A square root asks the question a square answers backwards: what number, multiplied by itself, gives this? Every number on this page is a perfect square, so every answer is whole — roots of numbers that are not perfect squares are a different topic, needing either a calculator or a method of estimation, and mixing them in makes it impossible to tell which skill is being tested. Turning on squares as well puts both directions on one page, which is the quickest way to make the inverse relationship obvious.
Who it suits
Grade 6 to Grade 9, ages eleven to fifteen. Recognising the squares up to 12 × 12 is the Grade 6 and 7 target; roots up to 25 are worth knowing before Pythagoras, where they turn up constantly.
How to use the settings
Set the largest root to match what the class is expected to recall — twelve covers the standard times table range, twenty-five covers everything that shows up in geometry. Switch on squares once roots alone are fluent: the mixed page tests whether a pupil is reading the symbol or pattern-matching on the numbers. Note that a small root limit and a long page force repeats — there are only so many perfect squares below 144 — so raise the limit or shorten the sheet if you want every question different.
What goes wrong
Halving instead of rooting is the commonest error, and it gives the right answer for exactly one number — four — which is enough to convince a pupil it works. The second is confusing the square root symbol with a division sign when working at speed. Both are caught quickly on a page with both directions.
Questions
- What is a perfect square?
- A number that is the square of a whole number: 1, 4, 9, 16, 25 and so on. Their roots are whole numbers, which is why this page uses only those.
- Why is the square root of 16 not 8?
- Because the root is the number that multiplies by itself to give 16, and 8 × 8 is 64. Four is the answer, since 4 × 4 is 16. Halving is not rooting.
- Do negative roots appear?
- No. Every positive number has two square roots, one positive and one negative, but the symbol √ means the positive one by convention, and that is what this page asks for.