Square and square roots-TEST 1

1. Without adding, find the sum: 1 + 3 + 5 + 7 + 9

16

9

36

25

The sum of consecutive odd numbers can be found by using the formula n^2, where n is the number of terms. In this case, there are 5 terms (1, 3, 5, 7, 9), so the sum is 5^2 = 25.

Explanation

The sum of consecutive odd numbers can be found by using the formula n^2, where n is the number of terms. In this case, there are 5 terms (1, 3, 5, 7, 9), so the sum is 5^2 = 25.

2. 196 is the square of

11

12

14

16

The correct answer is 14 because when you multiply 14 by itself, you get 196. In other words, 14 squared is equal to 196.

Explanation

The correct answer is 14 because when you multiply 14 by itself, you get 196. In other words, 14 squared is equal to 196.

3. Square of Which of the following would end with digit 1?

123

161

82

77

The square of a number will end with the digit 1 if the number itself ends with the digits 1, 9, or 5. In this case, the number 161 ends with the digit 1, so its square will also end with the digit 1. Therefore, the square of 161 will end with digit 1.

Explanation

The square of a number will end with the digit 1 if the number itself ends with the digits 1, 9, or 5. In this case, the number 161 ends with the digit 1, so its square will also end with the digit 1. Therefore, the square of 161 will end with digit 1.

4. The squares of which of the following would be odd numbers?

4352

2826

7775

82004

The square of a number is odd if and only if the number itself is odd. Therefore, the square of 7775 would be an odd number.

Explanation

The square of a number is odd if and only if the number itself is odd. Therefore, the square of 7775 would be an odd number.

5. Without doing any calculation, find the numbers which are surely perfect squares.

153

408

257

441

The number 441 is surely a perfect square because it is the square of 21. The other numbers cannot be determined without calculation.

Explanation

The number 441 is surely a perfect square because it is the square of 21. The other numbers cannot be determined without calculation.

6. A perfect square can never have the following digit at ones place

1

6

5

3

A perfect square can never have the digit 3 at its ones place because the square of any number ending in 3 will always have a ones digit of 9. For example, 3^2 = 9, 13^2 = 169, 23^2 = 529, and so on. Therefore, a perfect square can never end with the digit 3.

Explanation

A perfect square can never have the digit 3 at its ones place because the square of any number ending in 3 will always have a ones digit of 9. For example, 3^2 = 9, 13^2 = 169, 23^2 = 529, and so on. Therefore, a perfect square can never end with the digit 3.

7. Which of the following is not a perfect square?

1156

361

1128

1681

A perfect square is a number that can be expressed as the product of an integer multiplied by itself. To determine if a number is a perfect square, we can take its square root and check if it is an integer. In this case, the square root of 1156 is 34, the square root of 361 is 19, the square root of 1128 is approximately 33.57 (not an integer), and the square root of 1681 is 41. Therefore, 1128 is not a perfect square.

Explanation

A perfect square is a number that can be expressed as the product of an integer multiplied by itself. To determine if a number is a perfect square, we can take its square root and check if it is an integer. In this case, the square root of 1156 is 34, the square root of 361 is 19, the square root of 1128 is approximately 33.57 (not an integer), and the square root of 1681 is 41. Therefore, 1128 is not a perfect square.

8. Which of the following is a perfect square number?

2401

23453

222229

1057

2401 is a perfect square number because it is the square of 49. The square root of 2401 is 49, which means that 49 multiplied by itself equals 2401.

Explanation

2401 is a perfect square number because it is the square of 49. The square root of 2401 is 49, which means that 49 multiplied by itself equals 2401.

9. How many natural numbers lie between 18² and 19²?

35

38

36

63

To find the natural numbers between 18 squared and 19 squared, consider the sequence 18^2 + 1, 18^2 + 2, ..., 19^2 - 1. This is an arithmetic sequence with a common difference of 1. The number of terms in this sequence is (19^2 - 1) - (18^2 + 1) + 1 = 19^2 - 18^2 - 1 = 37 - 1 = 36.

Explanation

To find the natural numbers between 18 squared and 19 squared, consider the sequence 18^2 + 1, 18^2 + 2, ..., 19^2 - 1. This is an arithmetic sequence with a common difference of 1. The number of terms in this sequence is (19^2 - 1) - (18^2 + 1) + 1 = 19^2 - 18^2 - 1 = 37 - 1 = 36.

10. A number ending in 9 will have the units place of its square as

Option 13

9

1

3

When a number ending in 9 is squared, the units place of the square will always be 1. This is because when any number ending in 9 is multiplied by itself, the units digit of the product will always be 1. For example, 9 squared is 81, 19 squared is 361, and so on. Therefore, the correct answer is 1.

Explanation

When a number ending in 9 is squared, the units place of the square will always be 1. This is because when any number ending in 9 is multiplied by itself, the units digit of the product will always be 1. For example, 9 squared is 81, 19 squared is 361, and so on. Therefore, the correct answer is 1.

Square And Square Roots-test 1