Adding Consecutive Odd Numbers

Q.

How many factors of $1080$ are perfect squares?

Q.

What does $3$ factorial mean?

Q. Which of the following is a perfect cube?

1. 297
2. 144
3. 2744
4. 218

Q.

Express 144 as a sum of 12 odd numbers.

Q.

The cube of an even number is even and the cube of an odd number is odd.

1. True

2. False

Q. The number 8000 is a perfect cube.

1. True
2. False

Q. Difference of two numbers which are perfect cube is 189 . If the cube root of the smaller of the two numbers is 3, find the cube root of the larger number

Q.

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

1. 788

2. 784

3. 774

4. 441

Q. The cube root of square of 27 is _____

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

Q.

Find the odd one out from the following:

1. $9$

2. $16$

3. $64$

4. $100$

Q.

Find the cube roots of the following numbers by successive subtraction of numbers : 1, 7, 19, 37, 61 , 91, 127, 169, 217, 271, 331, 397 ...
(i) 64 (ii) 512 (iii) 1728

Q.

Find the smallest number that must be subtracted from those of the numbers in question 2, which are not perfect cubes, to make them perfect cubes. What are the coresponding cube roots?

Q. Find the cube root of the number 2460375 using the fact that $2460375=3375\times 729.$

1. 125
2. 135
3. 145
4. 155

Q. A cube of a number is 8 times the cube of another number. If the sum of the cubes of number is 243, then what is difference of the number?

Q. Every perfect cube number can be expressed as a sum of consecutive ______ numbers.

1. Even
2. Odd
3. Prime
4. Square

Q.

Find the cubes of the first five odd natural numbers and the cubes of the first five even natural numbers. What can you say about the parity of the odd cubes and even cubes?

Q. If 6³ is expressed as sum of consecutive odd numbers we get

1. 27+29+31+33+35+37
2. 31 +33+35+37+39+41
3. 31 + 33 + 35 + 37

Q. Evaluate: $125\sqrt[3]{3a^6}-\sqrt[3]{3125a^6}$

1. $200a^3$
2. $120a^2$
3. $a^3$
4. $20a$

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

2. 43, 45, 47, 49, 51, 53, 55

3. 39, 45, 47, 49, 51, 43, 59

4. 39, 45, 47, 49, 51, 53, 59

Q. Express 728 as a product of its prime factors.

1. $2^3\times 7\times 13$
2. $2^2\times 7^2\times 13$
3. $2^2\times 7\times 13$
4. $2^3\times 7^2\times 13$

Q. Question 1(x)
Find the cube root of each of the following numbers by prime factorization method:
91125

Q. 1, 03, 823 is a perfect cube. The units digit of cube root of 1, 03, 823 is ______.

1. 7
2. 9
3. 3
4. 5

Q.

State true or false.

(i) Cube of any odd number is even.

(ii) A perfect cube does not end with two zeroes.

(iii) If square of a number ends with 5, then its cube ends with 25.

(iv) There is no perfect cube which ends with 8.

(v) The cube of a two digit number may be a three digit number.

(vi) The cube of a two digit number may have seven or more digits.

(vii) The cube of a single digit number may be a single digit number.

Q.

Question 135

Evaluate: $\sqrt[3]{327}+\sqrt[3]{30.008}+\sqrt[3]{30.064}$

Q.

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

1. 9

2. 10

3. 11

4. 12

Q.

Question 90

Solve the following question:

Express 81 as the sum of first nine consecutive odd numbers.

Q.

What are the digits in the unit’s place of the cubes of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10? Is it possible to say that a number is not a perfect cube by looking at the digit in unit’s place of the given number, just like you did for squares?

Q.

How many times should the number 3 be multiplied with 648, in order to make it a perfect cube?

___

Q.

Express $5^3$ as a sum of 5 consecutive odd number.

1. 22, 23, 26, 27, 29

2. 21, 23, 25, 27, 29

3. 22, 23, 25, 27, 29

4. 22, 23, 25, 28, 29

Q. Express ${11}^3$ as the sum of consecutive odd numbers.

1. 66+77+88+99+110+121+132+143+154+165+176
2. 111+113+115+117+119+121+123+125+127+129+131
3. 121+123+125+127, 129+131+133+135+137+139+141
4. 101+103+105+107, 109+111+113+115+117+119+121