Interesting Patterns

Q.

Question 142

13 and 31 is a strange pair of numbers, such that their squares 169 and 961 are also a mirror image of each other. Can you find two other such pairs?

Q. Find the value of each of the following, using the column method:
1. $(23{)}^2$
2. $(35{)}^2$
3. $(52{)}^2$
4. $(96{)}^2$

Q.

Question 1 (i)
What will be the unit digit of the squares of the following number:

81

Q. Find the value of each of the following using the diagonal method:
1. $(67{)}^2$
2. $(86{)}^2$
3. $(137{)}^2$
4. $(256{)}^2$

Q. How many zeros at the end of a square of 400?

Q.

Write the 5th and 6th terms of triangular numbers. What square number do we get if we add these two numbers?Plz give the answer with details and step by step.

Q. Without doing actual addition, find the sum of:
$1+3+5+7+9+\dots +51+53$

Q.

Find the squares of the following numbers using diagonal method :

(i) 98 (ii) 273
(iii)348 (iv) 295
(v) 171

Q.

If a number ends with 3 zeroes, how many zeroes will its square have ?

Q. The number of zeros at the end of a perfect square is always __________.

Q.

Question 6

Write the correct answer from the given four options.

Which of the following cannot be a perfect square?

a) 841
b) 529
c) 198
d) All of these

Q.

Number of zeros in the square of 4000 is :

1. 6

2. 10

3. 4

4. 3

Q.

Question 141

A three-digit perfect square is such that, if it is viewed upside down, the number seen is also a perfect square. What is the number?

[Hint: The digits 1, 0 and 8 stay the same when viewed upside down, whereas 9 becomes 6 and 6 becomes 9].

Q.

If the square of a number ends with 10 zeroes, how many zeroes will the number have ?

Q.

The sum of two perfect squares is a perfect square. State whether the statement is true (T) or false (F).

1. True
2. False

Q. The sum of two consecutive numbers in a triangular number sequence is always a ______.

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

Q.

Question 2 (vi)
The following number is obviously not a perfect square. Give reasons.

89722

Q.

If a square ends with even number of zeros then a cube ends in odd number of zeros true or false

Q. 34. Prove that n(square root of n) is no a rational number, if n is not a perfect square

Q.

Question 6
Using the given pattern, find the missing numbers:
$1^2+2^2+2^2=3^2$
$2^2+3^2+6^2=7^2$
$3^2+4^2+{12}^2={13}^2$
$4^2+5^2+{\underset{–}{}}^2={21}^2$
$5^2+{\underset{–}{}}^2+{30}^2={31}^2$
$6^2+7^2+\underset{–}{}2=\underset{–}{}2$

Q.

Which of the following could be a perfect square?

1. 1681

2. 23453

3. 222222

4. 1057

Q.

Without doing te actual addition, find the sum of :

(i) 1+3+5+7+9+11+13+15+17+19+21+23

(ii) 1+3+5+7+9+....... +39+41

(iii) 1+3+5+7+9+........+51+53

Q.

Question 2 (iv)

The following number is obviously not a perfect square. Give reasons.

222222

Q.

Question 51

State whether the following statement is true or false:

The product of two perfect squares is a perfect square.

Q. Solve $(ab+1{)}^2$ - $(ab{)}^2$ where, b - a = 1.

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

Q.

An army base has some soldiers, such that when they stand in rows and columns they form a square. More soldiers were added to the camp and the number of rows and columns increased by 1. If there are 625 soldiers now, how many soldiers were added?

1. 54

2. 69

3. 64

4. 49

Q.

Question 1 (iv)
What will be the unit digit of the squares of the following number:

3853

Q. 25, 50, 100, 88: Of these numbers which is not a sum of two squares?

1. 25
2. 50
3. 100
4. 88

Q.

Is it possible for the square of a number to end with 5 zeroes? Give reason.

Q.

Question 1 (viii)
What will be the unit digit of the squares of the following number:

99880