Differences of Squares of Triangular Numbers and Converse

Q. The square of a natural number when subtracted from its cube results in 48. The number is:

1. 6
2. 5
3. 8
4. 4

Q.

Prove that the sum of cubes of three consecutive natural numbers is always divisible by 3.

Q.

The difference of cubes of two consecutive numbers is always divisible by 3.

1. True

2. False

Q. If the product of two numbers is 21 and their difference is 4, then the ratio of the sum of their cubes to the difference of their cubes is:

1. 185 : 165
2. 165 : 158
3. 185 : 158
4. 158 : 145

Q.

How can I find cube root of a 9 digit number

Q. The sum of the cubes of consecutive natural numbers gives the _______ of _________ numbers.

1. cubes, triangular
2. squares, prime
3. squares, triangular
4. cubes, prime

Q.

The difference of cubes of two concecutive numbers is always divisible by 3.

1. True

2. False

Q. The difference of the squares of two consecutive triangular numbers is always a _______.

1. Perfect square
2. Perfect cube
3. Prime number
4. Negative number.

Q. The sum of four consecutive odd numbers starting from 13 gives the cube of:

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

Q. Difference between squares of 10 and 6 is the cube of

1. 4
2. 5
3. 6

Q. Prove that for any positive integer n, n cube - n is divisible by 6

Q.

The sum of cubes of first five consecutive numbers starting from one is a perfect square of a number. Find the number.

___

Q.

Write the number of digits in cube root of the following cubes 491169069

Q.

Which of the following numbers is a cube number?

1. 36

2. 132

3. 81

4. 1728

Q.

Three numbers are in the ratio 1:2:3 . The sum of their cubes is 7776. Then difference between the biggest and smallest number is?

Q. How to use long division ➗ methods to find cube roots?

Q. When we take the difference between squares of consecutive triangular numbers, we get a ___.

Q.

The difference of cubes of two consecutive numbers is always divisible by 3.

1. True

2. False

Q. State true or false.
$6^2-3^2=3^3$

1. False
2. True

Q.

Find the cube root of $-12$.

Q. When we take the difference between squares of consecutive triangular numbers, we get a ___.

Q. After solving the equation $\frac{(5x+2{)}^2+(5x-2{)}^2}{(5x+2{)}^2-(5x-2{)}^2}=\frac{13}{12}$, solution set for $x$ is $\{m,0.27\}$. Then, the value of $m$ is:

Q. When we take the difference between squares of consecutive triangular numbers, we get a ___.

Q. If $2^{p+2}+2^{p+1}=96$, then find the value of $p$.

1. $1$
2. $2$
3. $3$
4. $4$
5. $5$

Q.

If the prime factorization of a number is 3x3x3x5x5x5, then its cube root is:

1. 25

2. 6

3. 9

4. 15

Q. The sum of cubes of first five consecutive numbers starting from one is a perfect square of

1. 15
2. 12
3. 9

Q. If${\left(\frac{m}{n}\right)}^{\frac{3}{8}}+{\left(\frac{n}{m}\right)}^{\frac{3}{8}}=-18$ then find value of ${\left(\frac{m}{n}\right)}^{\frac{1}{8}}+{\left(\frac{n}{m}\right)}^{\frac{1}{8}}$

1. $9$
2. $-9$
3. $3$
4. $-3$

Q. The square of a natural number when subtracted from its cube results in 48. The number is:

1. 6
2. 5
3. 4
4. 8

Q.

Cube of difference of two numbers remains same if we interchange the numbers.

1. True

2. False

Q. When we take the difference between squares of consecutive triangular numbers, we get _______.

1. perfect squares
2. perfect cubes
3. natural numbers
4. triangular numbers