8th Grade > Mathematics
CUBES AND CUBE ROOTS MCQs
Total Questions : 57
| Page 1 of 6 pages
Answer: Option A. -> 50653
:
A
The cube of an odd number is odd. Soonly 50653 is possible. We can alsocheck the answer bycalculatingthe cube of 37
= 37 × 37 × 37 = 50653.
:
A
The cube of an odd number is odd. Soonly 50653 is possible. We can alsocheck the answer bycalculatingthe cube of 37
= 37 × 37 × 37 = 50653.
Answer: Option B. -> False
:
B
The average of 3 and 7 is 5. The cube of 5 is 125.The cube of 3 and 7 is 27 and 343 respectively. The average of 27 and 343 is 185 which is not the cube of 5.
:
B
The average of 3 and 7 is 5. The cube of 5 is 125.The cube of 3 and 7 is 27 and 343 respectively. The average of 27 and 343 is 185 which is not the cube of 5.
Answer: Option A. -> 4
:
A
- 8 = - 2×−2×−2
3√−8=−2
- 216 = −6×−6×−6
3√−216=−6
So the given expression 3√−8−3√−216 becomes - 2 - (- 6) = - 2 + 6
= 4
:
A
- 8 = - 2×−2×−2
3√−8=−2
- 216 = −6×−6×−6
3√−216=−6
So the given expression 3√−8−3√−216 becomes - 2 - (- 6) = - 2 + 6
= 4
Answer: Option B. -> False
:
B
The cube of 3 = 27
The cube of 4 = 64
Since 30 lies between 27 & 64 so its cube root must lie between 3 & 4.
Hence, the given statement is false.
:
B
The cube of 3 = 27
The cube of 4 = 64
Since 30 lies between 27 & 64 so its cube root must lie between 3 & 4.
Hence, the given statement is false.
Answer: Option A. -> 2
:
A
The digit in the units place in 298 is 8.
cube of 8 is 512, which ends in 2.
Hence, the digit in the units place in the cube of 298 is 2
:
A
The digit in the units place in 298 is 8.
cube of 8 is 512, which ends in 2.
Hence, the digit in the units place in the cube of 298 is 2
Answer: Option A. -> a - b
:
A
Take a=2 and b=1 and check.
Alternatively, we know the algebraic identity,
a3−b3=(a−b)(a2+2ab+b2)
Hence , we can see that (a−b) is a factor of a3 - b3
Thus,a3 - b3is divisible by (a−b)
:
A
Take a=2 and b=1 and check.
Alternatively, we know the algebraic identity,
a3−b3=(a−b)(a2+2ab+b2)
Hence , we can see that (a−b) is a factor of a3 - b3
Thus,a3 - b3is divisible by (a−b)
Answer: Option A. -> 81
:
A
For every 10 mins passage of time, the number of students joining the class gets tripled i.e. multiplied by 3
The number of students joining after 40 minutes from now on is 729×3×3×3×3×3×3 ( from 20 mins back to 40 mins forward)
The cube root of 729 is 9.
Cube root of given number is 9×3×3=81
:
A
For every 10 mins passage of time, the number of students joining the class gets tripled i.e. multiplied by 3
The number of students joining after 40 minutes from now on is 729×3×3×3×3×3×3 ( from 20 mins back to 40 mins forward)
The cube root of 729 is 9.
Cube root of given number is 9×3×3=81
Answer: Option A. -> 784
:
A
Sum of cubes of first n natural numbers is(n(n+1))24
Putting n = 7,
(7(7+1))24
(7×8)24
= 784.
:
A
Sum of cubes of first n natural numbers is(n(n+1))24
Putting n = 7,
(7(7+1))24
(7×8)24
= 784.
Answer: Option A. -> 75
:
A
For a number to be a perfect cube, its prime factors should be in the form of triplets i.e. every prime factor should be raised to the power in multiples of 3
Prime factorizing the given number, we get 360=2×2×2×3×3×5
Hence, we can see that the given number must be multiplied by 3×5×5 i.e.75
:
A
For a number to be a perfect cube, its prime factors should be in the form of triplets i.e. every prime factor should be raised to the power in multiples of 3
Prime factorizing the given number, we get 360=2×2×2×3×3×5
Hence, we can see that the given number must be multiplied by 3×5×5 i.e.75
Answer: Option B. -> 729
:
B
By prime factorization,we get 729 = 3×3×3×3×3×3=36
So cube root of 729=(729)13=363=32=9
Since, the cube root of 729 is a natural number, 729 is a perfect cube.
:
B
By prime factorization,we get 729 = 3×3×3×3×3×3=36
So cube root of 729=(729)13=363=32=9
Since, the cube root of 729 is a natural number, 729 is a perfect cube.
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