Adding Triangular Numbers

Q.

What is the least number that should be added to $6200$to make it a perfect square?

Q. Find the Square of 56.

1. 3146
2. 3126
3. 3136
4. 5136

Q.

A number is called a triangular number if its dot pattern can be arranged in

1. a rectangle

2. a triangle

3. a rectangle and a line

4. a triangle and a rectangle

Q.

The sum of any two consecutive natural numbers is a perfect square.

1. a)Yes

2. a)No

Q.

What square number will we get if we add

13 and 14 triangular numbers

Q.

Question 139

Put three different numbers in the circles, so that when you add the numbers at the end of each line, you always get a perfect square.

Q.

find the squaresof the following, using property of perfect square.

(a) 7

(b) 15

Q. Write 121 as sum of two consecutive triangular numbers.

Q. Which of the following triangles represent a collection of triangular numbers?

1. A
2. B
3. C
4. D

Q.

Which of the following represents a circle of triangular numbers?

1. 

2. 

3. 

4. 

Q. Question 2
5t – 3 = 3t – 5

Q.

Construct a 3 × 3 magic square using all odd numbers from 1 to 17.

Q. In the following sequence of triangular numbers, how many dots will be present in the 5th (next) triangle?

1. 16
2. 12
3. 15
4. 14

Q.

Find the largest number of 3 digits which is a perfect square

Q. Find the value of
(i) 1 + 3 + 5 = _____
(ii) 1 + 3 + 5 + 7 + 9 +11 = ________
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 =_____

Q. The value of $(111111{)}^2$ is _____.

1. 12345654321
2. 12345432169
3. 12376589431
4. 13243563429

Q. If M is a square number, what is the next immediate square number?

1. $M+5$
2. $M+2\sqrt{M}+1$
3. $M^2+2M$
4. $M+2\sqrt{M}-1$

Q. Which of the following circles is a circle of triangular numbers ?

1. 
2. 
3. 
4. 

Q. The value of $(111111{)}^2$ is _____.

1. 12345654321
2. 12376589431
3. 12345432169
4. 13243563429

Q. Triangular number

Q.

Without adding, find the sum of $1+3+5+7+9$

1. $16$

2. $9$

3. $36$

4. $25$

Q.

The number representing both a square number and a triangular number is

1. $16$

2. $36$

3. $9$

4. $25$

Q. $8^3$ can be expressed as a sum of 8 consecutive odd integers.

1. True
2. False

Q.

The smallest natural number which when added to the difference of squares of 17 and 13 gives a perfect square is

Q.

If the product of four consecutive natural numbers increased by a natural number p is a perfect square, then the value of p is

1. 8

2. 4

3. 2

4. 1

Q.

Match the following:

$\begin{array}{cc}\text{a.)}\text{Interior angles on the same side of the transversal}& \left(i\right)1–5,2–6,3–7\text{and}4–8\\ \text{b.)}\text{Alternate exterior angles}& \left(ii\right)4–6,3–5\\ \text{c.)}\text{Corresponding angles}& \left(iii\right)1–7,2–8\\ \text{d.)}\text{Alternate interior angles}& \left(iv\right)3–6,4-5\end{array}$

Q.

The sum of any two consecutive natural numbers is a perfect square.

1. True

2. False

Q. The sum of first 14 odd numbers is _____.

1. 196
2. 197
3. 169
4. 145

Q.

The 6-th triangular number is:

A. 6

B. 10

C. 21

D. 28

Q. The sum of the first n consecutive natural numbers is a number.

1. negative
2. square
3. triangular
4. cubic