Real Number System MCQ Test — Class 9 IB MYP

Solution:

A rational number can be written as p/q where p and q are integers.

√2 = 1.41421356... is a non-terminating, non-repeating decimal, so it is irrational. — √2 ∉ ℚ

Solution:

Natural numbers: {1, 2, 3, ...} — does not include negatives.

Integers: {..., -3, -2, -1, 0, 1, 2, 3, ...} — includes -3. — -3 ∈ ℤ

Solution:

Factor 18 = 9 × 2 — √18 = √(9 × 2)

Take the square root of 9 out. — √(9 × 2) = 3√2

Solution:

0.333... is a repeating decimal.

It equals 1/3, which is a ratio of two integers. — 0.333... = 1/3 ∈ ℚ

Solution:

We need to find a number whose square is 49.

Since 7 × 7 = 49, we have √49 = 7. — 7² = 49, so √49 = 7

Solution:

Natural numbers: ℕ = {1, 2, 3, ...}

Whole numbers: W = {0, 1, 2, 3, ...}. So 0 ∈ W but 0 ∉ ℕ.

Solution:

Factor 50 = 25 × 2 — √50 = √(25 × 2)

Simplify. — √(25 × 2) = 5√2

Solution:

3² = 9 and 4² = 16, so √n is between 3 and 4 when 9 < n < 16.

√10 ≈ 3.16, which is between 3 and 4. — 9 < 10 < 16 ⟹ 3 < √10 < 4

Solution:

0.75 = 75/100

Simplify by dividing numerator and denominator by 25. — 75/100 = 3/4

Solution:

In the real number system, the square root of a negative number is not defined.

√(-4) is not a real number; it is imaginary. — √(-4) ∉ ℝ