Squares & Square Roots — Drills
Squares & Square Roots has 8 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 4 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Area — Space inside, measured in square units.
- Perfect square — A number that is some whole number squared: 1, 4, 9, 16, 25, …
- Square root — For k ≥ 0, √k is the nonnegative number whose square is k.
- Roots — The x values where y = 0.
Roots
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find √529.
Worked answer
23
23 × 23 = 529
Problem 2
Find √16.
Worked answer
4
4 × 4 = 16
Squares
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate 62.
Worked answer
36
6 × 6 = 36
Problem 2
Evaluate 122.
Worked answer
144
12 × 12 = 144
Decimal
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find √2.25.
Worked answer
1.5
1.5 × 1.5 = 2.25
Problem 2
Find √0.04.
Worked answer
0.2
0.2 × 0.2 = 0.04
Perfect
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Is 240 a perfect square?
- Yes
- No
Worked answer
No
152 = 225 and 162 = 256
240 sits between them, so no.
Problem 2
Is 100 a perfect square?
- Yes
- No
Worked answer
Yes
102 = 100, so yes.
Estimate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Estimate √213 to the nearest whole number.
Worked answer
15
142 = 196 and 152 = 225
213 is nearer 225
√213 ≈ 14.59
Problem 2
Estimate √305 to the nearest whole number.
Worked answer
17
172 = 289 and 182 = 324
305 is nearer 289
√305 ≈ 17.46
Simplifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Simplify √250 into the form a√10. What is a?
Worked answer
5
250 = 25 × 10
√25 × √10 = 5√10
Problem 2
Simplify √252 into the form a√7. What is a?
Worked answer
6
252 = 36 × 7
√36 × √7 = 6√7
Solving
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Solve x2 = 81.
- x = 9
- x = ± 9
- x = 81
- x = -9
Worked answer
x = ± 9
92 = 81 and (-9)2 = 81
An equation keeps both: x = ± 9
Note √81 on its own means just 9.
Problem 2
Solve x2 = 144.
- x = ± 12
- x = 144
- x = 12
- x = -12
Worked answer
x = ± 12
122 = 144 and (-12)2 = 144
An equation keeps both: x = ± 12
Note √144 on its own means just 12.
Fractions
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find √3664.
Worked answer
3/4
√36√64 = 68
= 34
Problem 2
Find √6436.
Worked answer
4/3
√64√36 = 86
= 43