Square root worksheets take students from perfect squares to cube roots, estimating, and solving equations like x2 = 49. These free printable square root worksheets give plenty of practice with the numbers that appear most often in grades 6 to 8, with an answer key on every PDF and a maker for new problems.
Quick answer: A square root is the number that, multiplied by itself, gives the original number: √49 = 7 because 7 × 7 = 49. A cube root uses three factors: ∛27 = 3. This page has 8 free square root worksheets (PDF) with answer keys for grades 6 to 8, plus a maker. Updated October 2026.
Ready-to-print samples
A few of the ready PDFs on this page. The full list is under Ready-to-print worksheets, and the maker above makes new problems on demand.
Perfect squaresLevel 1 with a full answer key.PDFCubes and cube rootsLevel 2 with a full answer key.PDFEstimate a square rootLevel 3 with a full answer key.PDFSolve x squared equals nLevel 4 with a full answer key.PDF
What is a square root?
Squaring a number multiplies it by itself, and a square root undoes that. The area of a square is its side times itself, so a square with area 49 square units has side √49 = 7 units. The symbol √ is called the radical sign, and the number under it is the radicand.
Perfect squares and cubes table
Knowing the first twelve squares and cubes makes root problems fast. Students should recognize these without a calculator:
n
n2 (square)
n3 (cube)
1
1
1
2
4
8
3
9
27
4
16
64
5
25
125
6
36
216
7
49
343
8
64
512
9
81
729
10
100
1,000
11
121
1,331
12
144
1,728
Square root worksheet: worked examples
Roots of perfect squares, cubes, fractions and decimals all follow the same question: what multiplies to give this number?
Root
Question it asks
Answer
√49
What number times itself is 49?
7
√144
What number times itself is 144?
12
√(81/16)
Take the root of top and bottom
9/4
∛27
What number cubed is 27?
3
∛125
What number cubed is 125?
5
√0.25
What decimal times itself is 0.25?
0.5
Estimating square roots worksheet
Most numbers are not perfect squares, so their roots are decimals that never end. To estimate, find the two perfect squares on either side:
Root
Nearest perfect squares
So it is
Calculator value
√10
9 and 16
Between 3 and 4
3.16
√20
16 and 25
Between 4 and 5
4.47
√30
25 and 36
Between 5 and 6
5.48
√50
49 and 64
Between 7 and 8
7.07
√75
64 and 81
Between 8 and 9
8.66
√99
81 and 100
Between 9 and 10
9.95
Try ten square root problems
Use these as a warm-up. Give both roots when solving x2 = n.
#
Problem
Answer
1
√64
8
2
√169
13
3
∛64
4
4
∛1,000
10
5
√0.04
0.2
6
√(25/36)
5/6
7
√225
15
8
x2 = 49
x = 7 or x = -7
9
√50 is between
7 and 8
10
∛216
6
Square root vocabulary
Students answer questions faster when they know the words. These are the terms used on the worksheets and answer keys:
Word
Meaning
Example
Square root
A number that multiplied by itself gives the original
√36 = 6
Perfect square
A number with a whole-number square root
1, 4, 9, 16, 25
Radicand
The number under the radical sign
36 in √36
Cube root
A number that used three times as a factor gives the original
∛8 = 2
Irrational number
A number whose decimal never ends or repeats
√2 ≈ 1.414
Square roots worksheet, practice and PDFs
This page is also searched as square roots worksheet, square roots practice, perfect squares worksheet, cube roots worksheet, estimating square roots worksheet and square and cube roots worksheet. All of them are the free PDFs above, with an answer key, for US Letter or A4, with no sign-up. The exponents worksheets page covers the powers behind these roots.
Use square root and cube root symbols to solve x2 = p and x3 = p
Grade 8
8.NS.A.2
Use rational approximations of irrational numbers, such as √2
Grade 6
6.EE.A.1
Evaluate expressions with exponents (squares and cubes)
Common mistakes with square roots
Mistake
Example
Fix
Halving the number
√36 = 18
Ask what times itself is 36: 6
Forgetting the negative root
x2 = 25, so x = 5
Both 5 and -5 work: x = ±5
Taking the root of a sum
√(9 + 16) = 3 + 4
Add first: √25 = 5
Confusing square and cube roots
∛8 = 4
The cube root of 8 is 2, because 2 × 2 × 2 = 8
Not estimating
√20 = 10
Between 4 and 5, because 16 < 20 < 25
Real-life uses of square roots
Square roots appear wherever area, distance or speed is involved:
Situation
Calculation
Answer
Side of a square garden with area 144 m²
√144
12 m
Side of a square tile with area 2.25 ft²
√2.25
1.5 ft
Edge of a cube-shaped box with volume 125 cm³
∛125
5 cm
Diagonal distance on a grid, 3 across and 4 up
√(9 + 16)
5 units
Side of a square with area 30 ft²
√30
about 5.5 ft
Which square root worksheet should you start with?
Start with perfect squares until students know them by heart, then add cube roots, estimating and equations. Set B gives a retest for the first three levels.
Level
Skill
Best for
Level 1
Perfect squares
Grades 6 and 7
Level 2
Cubes and cube roots
Grade 8
Level 3
Estimate a square root
Grade 8
Level 4
Solve x2 = n
Grade 8
Level 5
Mixed roots
Grade 8 review
A weekly plan for square roots
Day
Focus
Suggested block
Monday
Perfect squares and roots
15 min
Tuesday
Cubes and cube roots
15 min
Wednesday
Estimating roots
15 min
Thursday
Solving x2 = n
15 min
Weekly total
Four short sessions
60 min
Frequently asked questions
5 quick answers
Where can I download free square root worksheets?
Open any worksheet in the Ready-to-print list on this page, choose US Letter or A4, then print or save the PDF. They are free, with answer keys, and no account is needed.
How do you find a square root?
Ask which number times itself gives the number under the radical. For example, √64 = 8 because 8 × 8 = 64.
How do you estimate a square root?
Find the two perfect squares on either side. For √20, 16 and 25 are on either side, so the root is between 4 and 5, nearer 4.5.
What is a cube root?
It is the number that, used as a factor three times, gives the original. ∛27 = 3 because 3 × 3 × 3 = 27.
What grade learns square roots?
Squares and cubes appear in grade 6, and square roots, cube roots and irrational numbers are taught in grade 8.
