Verifying the Given Number is Cube Number

Q. Find the cube root of 10648 by prime factorisation method.

Q. The smallest number that should be multiplied with 32 to make it a perfect cube is _____.

1. 2
2. 4
3. 3
4. 6

Q.

If a and b are coprime, what should $a^3$ $b^2$ be multiplied with to make it a perfect cube?

1. $b^3$

2. $b$

3. $a^3$

4. $a^2$ $b$

Q.

Which of the following numbers is a triangular number with its square ending with 4?

1. 6

2. 24

3. 8

4. 28

Q. Find the cube root of 10648 by prime factorisation method.

Q.

If a and b are coprime, what should $a^3$ $b^2$ be multiplied with to make it a perfect cube?

1. $a^3$

2. $b^3$

3. $b$
4. $a^2$ $b$

Q.

Question 54

State whether the following statement is true or false:

Each prime factor appears 3 times in its cube.

Q. What should be multiplied with $x^2{y}^3$ to make it a perfect cube, if $x$ and $y$ are prime numbers?

1. $x^2$
2. $x$
3. $x^3$
4. $xy$

Q. Find the smallest number by which $135$ must be divided to obtain a perfect cube.
[3 marks]
[NCERT - Ex 7.1, Q3 (iii)]
[Smallest Multiple that is a Perfect Cube]

1. 5
2. 3
3. 2
4. 6

Q.

Which number should divide $(7^3-8^2-87)$ to make it a perfect cube?
(A) 2
(B) 3
(C) 5
(D) 7

Q.

Q.

Which of the following represents a circle of triangular numbers?

1. 

2. 

3. 

4. 

Q. If a cube number is prime factorised as a x a x a x b x b x c, which of the following is true?

1. b = c
2. b = 2c
3. b < c
4. b > c

Q. If one edge of a cube measures 4 cm, the volume of the cube is:

1. 64 cc
2. 36 cc
3. 216 cc
4. 81 cc

Q.

The sum of two consecutive triangular numbers gives a __ number.

Q. If the unit digit of a number is 3, then the unit digit of its cube is:

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

Q.

Which of the following represents a circle of triangular numbers?

1. 

2. 

3. 

4. 

Q. If there are 27912 people to be arranged in the form of a square, how many people should be left out?

1. 18
2. 23
3. 7
4. 12

Q. should be multiplied with $a^3$ $b^2$ to make it a perfect cube, if a and b are prime numbers?

1. a${}^3$
2. a${}^2$b
3. b

Q. A product of two numbers is given as $x^4{y}^2$, such that $x$ and $y$ are positive integers. Which of the following should be multiplied with the given product to make it a perfect cube?

1. $x^6{y}^3$
2. $xy$
3. $x^{2}y$
4. $y$

Q. Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:

1. $1323$
2. $7803$
3. $35721$
4. $2560$

Q. Pair the following numbers with the correct prime factorization of their cube roots.

1. 64
2. 216
3. 512
4. 2 x 3
5. 2 x 2 x 2
6. 2 x 2

Q. Pair the following numbers with the correct prime factorization of their cube roots.

1. 64
2. 216
3. 512
4. 2x3
5. 2x2x2
6. 2x2

Q. Find the square root of $0.0169$

1. $0.13$
2. $0.15$
3. $0.14$
4. $0.16$

Q. The sum of two consecutive triangular numbers gives a __ number always.

1. triangular
2. square
3. even
4. odd