In a quiz, a student was asked to find a number that is:
i) Irrational
ii) Greater than 2 but less than 3
iii) Whose square is also irrational
Which of the following could be the number?
Show answer & explanation
Correct answer: B
Explanation
Correct — Option 2 (√10 − 1) is right. Let's verify each:
Option 1: √5 ≈ 2.236
- Irrational ✓, between 2 and 3 ✓
- Square = 5 → rational ✗ (fails condition iii)
Option 2: √10 − 1 ≈ 2.162
- Irrational ✓ (√10 is irrational, subtracting 1 keeps it irrational)
- Between 2 and 3 ✓
- Square = (√10 − 1)² = 10 − 2√10 + 1 = 11 − 2√10 → irrational ✓ (since √10 is irrational)
- Satisfies all three conditions ✓
Option 3: 2.5
- Rational ✗ (fails condition i immediately)
Option 4: √4.5 ≈ 2.121
- Irrational ✓, between 2 and 3 ✓
- Square = 4.5 → rational ✗ (fails condition iii)
So Option 2 is the only one satisfying all three conditions. The marked answer is correct.