Solved in the same order as the textbook — Exercise Set by Exercise Set.
Exercise 6.2
Q1. In this case, which statement about the prime factors of 4 is correct for a rational number with denominator 4 in lowest form?
✓ Its decimal expansion terminates
○ It must be irrational
○ It cannot be represented as a fraction
○ 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. In this case, which of the following is irrational?
○ Ö49
○ 7/1
✓ Ö7
○ 7
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 37 is divided by 11?
○ 5
○ 3
○ 7
✓ 4
Solution: Since 37 = 11 × 3 + 4, the remainder is 4. — Examisthan.com
Q4. Consider the same result: what is the HCF of 12 and 18?
○ 4
○ 8
✓ 6
○ 36
Solution: The greatest common divisor of 12 and 18 is 6. — Examisthan.com
Q5. Consider the same result: what is the LCM of 12 and 18?
✓ 36
○ 42
○ 216
○ 30
Solution: Using LCM × HCF = product for two positive integers, the LCM is 36. — Examisthan.com