Perfect square — Grade 7 Math, what it means and where it is taught
A number that is some whole number squared: 1, 4, 9, 16, 25, …
Taught in Grade 7 Math.
Where it is taught
What uses it later
This idea is needed for:
- Completing the square — Rewriting x2 + bx as a perfect square minus a constant.
- Simplest radical form — No perfect square factors left under the root.
Practise this idea
11 questions in the course bank use Perfect square, in Problem Solving, Squares & Square Roots, Real Numbers, Expressions, Structure & Units, Factoring, Solving Quadratic Equations. The first 8 are below; the rest are in those units.
Problem 1
What comes next in 1, 4, 9, 16, …?
Worked answer
25
12, 22, 32, 42, …
Next is 52 = 25
Problem 2
Find √121.
Worked answer
11
11 × 11 = 121
Problem 3
Is 50 a perfect square?
- Yes
- No
Worked answer
No
50 sits between 49 and 64, so no whole number squares to it.
Problem 4
√40 lies between which two consecutive whole numbers?
- 5 and 6
- 6 and 7
- 7 and 8
- 19 and 21
Worked answer
6 and 7
36 < 40 < 49
62 = 36 and 72 = 49
So 6 < √40 < 7
Problem 5
Simplify √72 into the form a√2. What is a?
Worked answer
6
72 = 36 × 2
√72 = √36 × √2 = 6√2
Problem 6
Classify √9.
- Rational
- Irrational
Worked answer
Rational
√9 = 3, a whole number, so rational.
Problem 7
Classify √7.
- Rational
- Irrational
Worked answer
Irrational
7 is not a perfect square
√7 = 2.6457… never repeats, so irrational.
Problem 8
Which of these is irrational?
- 0.25
- 23
- √16
- √11
Worked answer
√11
0.25 and 23 are fractions, so rational
√16 = 4, rational
11 is not a perfect square, so √11 is irrational.