Irrational — Grade 7 Math, what it means and where it is taught

A real number that cannot be written as a fraction — its decimal never repeats and never ends.

Taught in Grade 7 Math.

Where it is taught

Practise this idea

9 questions in the course bank use Irrational, in Real Numbers, Pythagorean Theorem, Radicals & Rational Exponents. The first 8 are below; the rest are in those units.

Problem 1

Classify √9.

  1. Rational
  2. Irrational
Worked answer

Rational

√9 = 3, a whole number, so rational.

Problem 2

Classify √7.

  1. Rational
  2. Irrational
Worked answer

Irrational

7 is not a perfect square

√7 = 2.6457… never repeats, so irrational.

Problem 3

Which of these is irrational?

  1. 0.25
  2. 23
  3. √16
  4. √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.

Problem 4

Which describes 0?

  1. Integer and rational
  2. Irrational
  3. Neither
Worked answer

Integer and rational

0 is a whole number and an integer

It is rational because 0 = 01.

Problem 5

Is the sum of two irrational numbers always irrational?

  1. Yes, always
  2. No — it can be rational
Worked answer

No — it can be rational

√2 + (-√2) = 0, which is rational

So the sum is not always irrational

It usually is — but "always" is too strong.

Problem 6

A right triangle has both legs equal to 1. What is its hypotenuse?

  1. 1
  2. 2
  3. √2
  4. √3
Worked answer

√2

12 + 12 = 2

c = √2 ≈ 1.414 — an irrational number.

Problem 7

Which sum is irrational?

  1. 3 + √2
  2. √4 + √9
  3. 12 + 13
  4. √16 - 1
Worked answer

3 + √2

√2 is irrational and 3 is rational

So the sum is irrational

All the others reduce to rationals

Problem 8

Expand (√3 + 2)(√3 - 2).

Worked answer

-1

(√3)2 - 22

= 3 - 4 = -1

A rational answer from irrational parts

Elsewhere

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