Patterns in Square Differences

Q.

Which one of the following cannot be the square of a natural number?

1. 32761

2. 81225

3. 20164

4. 42437

Q. What is the square of 84?

1. 7056

Q. The square of the number 33 is .

1. 889
2. 1089
3. 729
4. 1239

Q.

What is the units digit of the square of 56789?

1. 1

2. 4

3. 9

4. 6

Q.

The value of ${100}^2-{99}^2$ is equal to

1. 199

2. 200

3. 201

4. 198

Q.

What is the square of the number $89$?

Q. What should be the smallest integer that multiplies with 245 to make it a perfect square?

1. 1
2. 5
3. 10
4. 15

Q.

If 24, $x$, 26 form a pythagorean triplet with 26 being the largest number, then find the value of $x$.

1. 8

2. 11

3. 9

4. 10

Q.

The value of $(n+1{)}^2-n^2$ is equal to

1. $2n+2$

2. $n+1$

3. $n+2$

4. $2n+1$

Q. Find the Pythagorean triplets among the following sets of numbers.
(i)3, 4, 5
(ii) 9, 40, 41
(iii) 4, 7, 8

Q.

Which of the following cannot be a factor of any positive number?

1. 1

2. The number itself

3. 0

4. Square of the integer​

Q. Find the remaining members of a Pythagorean triplet whose smallest member is 8.

1. 14, 15
2. 14, 16
3. 15, 17
4. 15, 16

Q.

All numbers of a Pythagorean triplet are odd. State whether the statement is true (T) or false (F).

1. True
2. False

Q.

The value of ${55}^2-{54}^2$ is equal to

1. $109$

2. $119$

3. $129$

4. $111$

Q.

The value of ${72}^2-{71}^2$ is equal to

1. $145$

2. $147$

3. $148$

4. $143$

Q. Which among the following are Pythagorean triplets?

1. 1, 1, 2
2. 3, 4, 5
3. 12, 16, 20
4. 15, 8, 17

Q.

The value of ${62}^2-{61}^2$ is equal to

1. 121

2. 123

3. 124

4. 122

Q. If the difference between the squares of two alternate natural numbers $a$ and $b$ is 300. Find the value of $\frac{a+b}{2}$.

1. 300
2. 150
3. 75
4. 37.5

Q. If the square of the number $A5$ is $X25$, then $X$ is equal to .

1. $A(A-1)$
2. $A(A+1)$
3. $2A+2$
4. $2A-2$

Q.

If ${75}^2-{74}^2=75+x$, then the value of $x$ is equal to

1. 74

2. 75

3. 76

4. 77

Q. If $8^5=32768$, then the value of ${0.8}^5$ is .

1. 3.2768
2. 0.32768
3. 32768
4. 32779

Q. Think of a positive number, say $x$. From the square of this number, subtract three times of itself. If the result is $10$, then $x$ is equal to

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

Q. Choose the correct pairs of numbers and their squares.

1. 11
2. 19
3. 16
4. 121
5. 256
6. 381
7. 8
8. 64

Q.

Find the squares of these numbers:

(i) 30

(ii) 400

(iii) 7000

(iv) 6 × 10²⁵

Q.

The value of ${201}^2-{200}^2$ is equal to

1. $401$

2. $403$

3. $404$

4. $402$

Q. If the exponent of a number in scientific notation is ______, then to get the number in standard notation, the decimal point is moved to the ______.

1. Both A and C
2. negative , right
3. positive, right
4. negative, left

Q. If $8^5=32768$, then the value of ${0.8}^5$ is ____ .

1. 3.2768
2. 0.32768
3. 32768
4. 32779

Q. How to simplify $(2.3\times {10}^{-6})(3.1\times {10}^{-2})$ in scientific notation?

Q. The sum of $a$ and $b$ is $132$. If $a$ is the square of $b$ and the product of $a$ and $b$ is negative, what is $a$?

1. -12
2. 121
3. 144
4. 11

Q.

Mention the squares of (a) +7 (b) (−4)