Solved in the same order as the textbook — Exercise Set by Exercise Set.
Exercise 6.2
Q1. Consider the same result: which statement about the prime factors of 12 is correct for a rational number with denominator 12 in lowest form?
○ It cannot be represented as a fraction
✓ Its decimal expansion terminates
○ It must be irrational
○ Its decimal expansion is non-terminating recurring
Solution: A rational number has a terminating decimal expansion when the denominator in lowest form has no prime factors other than 2 and 5. — Examisthan.com
Q2. Consider the same result: which of the following is irrational?
○ 2/1
○ 2
○ Ö4
✓ Ö2
Solution: The square root of a prime number is irrational. — Examisthan.com
Q3. Consider the same result: using Euclid's division algorithm, what is the remainder when 44 is divided by 13?
○ 8
✓ 5
○ 4
○ 6
Solution: Since 44 = 13 × 3 + 5, the remainder is 5. — Examisthan.com
Q4. Consider the same result: what is the HCF of 18 and 22?
○ 4
○ 198
○ 1
✓ 2
Solution: The greatest common divisor of 18 and 22 is 2. — Examisthan.com
Q5. Consider the same result: what is the LCM of 18 and 22?
○ 200
✓ 198
○ 196
○ 396
Solution: Using LCM × HCF = product for two positive integers, the LCM is 198. — Examisthan.com