Answer :
Certainly! Let's analyze each statement one by one and determine whether they are TRUE or FALSE:
1.1 The first three multiples of 20 are: 20, 40, 60.
- Multiples of a number are found by multiplying it by integers. The first three multiples of 20 are:
- 20 × 1 = 20
- 20 × 2 = 40
- 20 × 3 = 60
- Therefore, the statement is TRUE.
1.2 √(64 + 36) > ³√27
- Let's compute each part:
- √(64 + 36) = √100 = 10
- ³√27 is the cube root of 27, which is 3.
- Since 10 is greater than 3, the inequality holds true. Therefore, this statement is TRUE.
1.3 ab = ba
- In arithmetic, multiplication is commutative, which means the order of factors does not change the product.
- So, ab = ba holds true for any numbers a and b. Therefore, this statement is TRUE.
1.4 The values have been written in descending order: 0.3; √(³√0.001); (0.2)³
- Let's evaluate each value:
- 0.3 is 0.3.
- ³√0.001 = (0.001)^(1/3) = 0.1
- (0.2)³ = 0.008
- In descending order: 0.3, 0.1, 0.008, which matches the sequence given. Therefore, this statement is TRUE.
1.5 c/d < d/c
- Without specific values of c and d, we can't definitively say if this relationship is true. Generally, this inequality holds only if both c and d are positive and c is not equal to d, with particular magnitude relations. Based on the provided results, the inequality d/c > c/d holds, making this statement FALSE.
1.6 2³ + 2² = 4⁵
- Calculate each side:
- 2³ = 8, 2² = 4, thus 2³ + 2² = 8 + 4 = 12
- 4⁵ = 1024
- 12 is not equal to 1024. Therefore, this statement is FALSE.
1.7 3x⁵ 4x² = 12x¹⁰
- Simplify the left side:
- 3x⁵ 4x² = (3 4) x^(5 + 2) = 12x⁷
- 12x⁷ is not equal to 12x¹⁰. Therefore, this statement is FALSE.
1.8 (3ab)² = 6a²b²
- Expand the left side:
- (3ab)² = (3²)(a²)(b²) = 9a²b²
- 9a²b² is not equal to 6a²b². Therefore, this statement is FALSE.
To summarize:
1.1 TRUE
1.2 TRUE
1.3 TRUE
1.4 TRUE
1.5 FALSE
1.6 FALSE
1.7 FALSE
1.8 FALSE
1.1 The first three multiples of 20 are: 20, 40, 60.
- Multiples of a number are found by multiplying it by integers. The first three multiples of 20 are:
- 20 × 1 = 20
- 20 × 2 = 40
- 20 × 3 = 60
- Therefore, the statement is TRUE.
1.2 √(64 + 36) > ³√27
- Let's compute each part:
- √(64 + 36) = √100 = 10
- ³√27 is the cube root of 27, which is 3.
- Since 10 is greater than 3, the inequality holds true. Therefore, this statement is TRUE.
1.3 ab = ba
- In arithmetic, multiplication is commutative, which means the order of factors does not change the product.
- So, ab = ba holds true for any numbers a and b. Therefore, this statement is TRUE.
1.4 The values have been written in descending order: 0.3; √(³√0.001); (0.2)³
- Let's evaluate each value:
- 0.3 is 0.3.
- ³√0.001 = (0.001)^(1/3) = 0.1
- (0.2)³ = 0.008
- In descending order: 0.3, 0.1, 0.008, which matches the sequence given. Therefore, this statement is TRUE.
1.5 c/d < d/c
- Without specific values of c and d, we can't definitively say if this relationship is true. Generally, this inequality holds only if both c and d are positive and c is not equal to d, with particular magnitude relations. Based on the provided results, the inequality d/c > c/d holds, making this statement FALSE.
1.6 2³ + 2² = 4⁵
- Calculate each side:
- 2³ = 8, 2² = 4, thus 2³ + 2² = 8 + 4 = 12
- 4⁵ = 1024
- 12 is not equal to 1024. Therefore, this statement is FALSE.
1.7 3x⁵ 4x² = 12x¹⁰
- Simplify the left side:
- 3x⁵ 4x² = (3 4) x^(5 + 2) = 12x⁷
- 12x⁷ is not equal to 12x¹⁰. Therefore, this statement is FALSE.
1.8 (3ab)² = 6a²b²
- Expand the left side:
- (3ab)² = (3²)(a²)(b²) = 9a²b²
- 9a²b² is not equal to 6a²b². Therefore, this statement is FALSE.
To summarize:
1.1 TRUE
1.2 TRUE
1.3 TRUE
1.4 TRUE
1.5 FALSE
1.6 FALSE
1.7 FALSE
1.8 FALSE
