Adding Consecutive Odd Numbers

Q.

Shishir is trying to express every cube as the sum of consecutive odd numbers. He is struggling to express $7^3$ in this way. Can you find the odd numbers whose sum leads to $7^3$?

1. 39, 45, 47, 49, 51, 53, 59

2. 43, 45, 41, 49, 57, 53, 55

3. 43, 45, 47, 49, 51, 53, 55

4. 39, 45, 47, 49, 51, 43, 59

Q. While trying to express $7^3$ as the sum of consecutive odd numbers, after finding the middle number(s) what is the next step?

1. Find the odd numbers which give a sum of 49.
2. Find 7 consecutive odd numbers after 49.
3. Find 3 consecutive odd numbers on either side of 49.
4. None of these

Q. While trying to express $7^3$ as the sum of consecutive odd numbers, what is the number, $7^3$ should be divided by to find the middle number?

1. 48, 50
2. 49
3. 46, 48
4. 47, 49

Q.

What is the sum of the cubes of the first 7 natural numbers?

1. 788

2. 784

3. 774

4. 441

Q. Find the sum of 1 + 3 + 5 + 7 + 9, without performing the actual summation.

1. 64
2. 25
3. 15
4. 21

Q. Express $9^3$ as the sum of 9 consecutive odd numbers.

1. 71, 73, 75, 77, 79, 81, 83, 85 and 87
2. 81, 83, 85, 87, 89, 91, 93, 95 and 97
3. 91, 93, 95, 97, 99, 101, 103, 105 and 107
4. 73, 75, 77., 79, 81, 83, 85, 87, and 89.

Q.

What is the smallest number by which 392 must be multiplied, so that the product is a perfect cube?

1. 7

2. 6

3. 4

4. 5

Q.

What is the least number by which 10125 should be divided so that the quotient is a perfect cube?

1. 2

2. 3

3. 4

4. 5

Q.

$9^3$ can be represented as a sum of how many consecutive odd number?

1. 11

2. 12

3. 9

4. 10

Q. The cube root of square of 27 is _____

1. 27
2. 729
3. 3
4. 9