This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Properties of Squares”.

1. ________ is the square of 25.

a) 625

b) 525

c) 125

d) 655

View Answer

Explanation: A square of any number is the product which is obtained by multiplying the number with itself. So, here 25×25=625. Hence the answer would be 625, and the others would be incorrect.

2. Which of the following is a triangular number?

a) 2

b) 4

c) 5

d) 6

View Answer

Explanation: Triangular numbers are the numbers which when arranged in increasing order forms a shape of triangle, the triangle shown represents the number 6. Hence the only number forming the triangular number is 6. Hence the options other than 6 are incorrect.

3. Which of the following is not a triangular number?

a) 1

b) 10

c) 15

d) 20

View Answer

Explanation: Triangular numbers are the numbers which when arranged in increasing order forms a shape of triangle. Here the options other than 20 form triangular numbers. Hence the correct option would be 20, since it does not form a triangular number.

4. If a number has 1 in it’s one’s place, what can be it’s square?

a) 91

b) 144

c) 169

d) 121

View Answer

Explanation: We know that if a number has 1 in it’s one’s place the square of that particular number would also have 1 in it’s one’s place. Here there are two options that can be correct but the option 91 couldn’t be correct because it isn’t a perfect square. Therefore the correct option would be 121.

5. Which of the following cannot be a square of the number of with 4 at it’s one’s place?

a) 4

b) 196

c) 36

d) 144

View Answer

Explanation: We know that the number which has 4 in it’s one’s place has it’s ending with 6 in it’s one’s place. Here 36 cannot be the correct answer since it is square of 6. Here the correct answer is 196 as it is square of 14.

6. If we add two triangular numbers what would be the result?

a) Square

b) Square Root

c) Cube

d) Cube Root

View Answer

Explanation: If we add two triangular numbers then the sum would be a perfect square.

For example: 1 and 3 are triangular number when added to each other gives 4, 4 is a perfect square.

7. There are _____ non-square numbers between square of 5 and 6.

a) 11

b) 12

c) 13

d) 10

View Answer

Explanation: The non-square numbers are the number which aren’t perfect squares, therefore the numbers between the square of 5 and 6 (i.e. 25 and 36) is 10 the numbers are 26, 27, 28, 29, 30, 31, 32, 33, 34 and 35.

8. If we add the first n odd numbers we get ______

a) n^{2}

b) 2n

c) 3n

d) n

View Answer

Explanation: When we add first n odd numbers we get, n

^{2}.

For example: the first 5 odd numbers are 1, 3, 5, 7 and 9

When we add them, we get, 1+3+5+7+9+=25. We know that 25 is the square of number 5. Hence, we find that when first n numbers are added we get n

^{2}.

9. How can one express 144 in terms of squares?

a) 12^{2}-1

b) 144-1

c) 13^{2}-1

d) 142+1

View Answer

Explanation: Here all the options other then 13

^{2}-1 give 143 as their answer but only 12

^{2}-1 gives

it in the form of squares. Hence the correct answer would be 12

^{2}-1.

10. If square of 11 is 121 then, what is the square of 111?

a) 121

b) 12321

c) 1234321

d) 123321

View Answer

Explanation: The squares of the numbers containing one on all places show a very beautiful pattern.

The pattern is as follows, 11

^{2}=121 => 111

^{2}=12321. Hence students can use this pattern to calculate the squares of all the numbers having 1 on it’s all places.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 8**.

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