6

Q1. What is the square of 508?

• 317564
• 358064
• 258064
• 250864

Solution

Q2. 205² can be found by visual method taking a and b as _______ and _______.

• 20, 5
• 2, 5
• 200, 5
• 25, 5

Solution

205² = 200 + 5 Thus, a = 200 and b = 5

Q3. Estimated value of the square root of 10 to the nearest whole number is

• 3
• 4
• 5
• 6

Solution

Q4. If the sides of a rectangle are 25 cm and 16 cm then the side of a square whose area is equal to the area of this rectangle is:

• 40 cm
• 30 cm
• 4 cm
• 20 cm

Solution

Area of square = Area of rectangle = 25 x 16 cm2 = 400 cm2 400 = 2 x 2 x 2 x 2 x 5 x 5 Side of the square = 2 x 2 x 5 = 20 cm

Q5. A number has 4 zeroes at the end. How many zeroes will its square have?

• 8
• 16
• 2
• 4

Solution

If a natural number has n zeroes at the end, its square have 2n zeroes at the end. So, the square of the number with 4 zeroes at the end will have 8 zeroes at the end.

Q6. By which number, should 588 be multiplied so as to get a perfect square?

• 2
• 3
• 5
• 7

Solution

We have: 588 = 2 x 2 x 3 x 7 x 7 As the prime factor 3 has no pair, 588 is not a perfect square. If 3 gets a pair, then the number will become a perfect square. Therefore, 588 has to be multiplied with 3 to obtain a perfect square. Therefore, 588 x 3 = 1764 is a perfect square.

Q7. Square root of 10.24 is:

• 0.32
• 3.2
• 3.02
• 3.002

Solution

  Square root of 10.24 is 3.2.

Q8. Which of the following is not a triangular number?

• 3
• 6
• 10
• 11

Solution

11 is not a triangular number.

Q9. Which of the following is a triangular number?

• 0
• 1
• 2
• -1

Solution

1 is a triangular number.

Q10. If a number has 1 or 9 in the unit's place, then it's square ends in

• 1
• 3
• 8
• 9

Solution

If a number has 1 or 9 in the unit's place, then it's square ends in 1.

Q11. The square root of 123454321 is ______ .

• 111111
• 111
• 1111
• 11111

Solution

Observe the following pattern: 1² = 1 11² = 121 111² = 12321 1111² = 1234321 11111² = 123454321 Thus, the square root of 123454321 is 11111.

Q12. The sum of first 5 consecutive odd numbers is:

• 16
• 18
• 25
• 36

Solution

We know that the sum of first n odd natural numbers is n². Thus, sum of first 5 consecutive odd numbers = 5²= 25.

Q13. The whole number whose square is nearer to the number 140 is:

• 11
• 12
• 13
• 14

Solution

We have: 121 < 140 < 144 Also, 112= 121 and 122= 144 Clearly, 140 is closer to 144 than 121.Thus, the required whole number whose square is nearer to the number 140 is 12.

Q14. The square of the number 65 is

• 3175
• 4215
• 3225
• 4225

Solution

Q15. Square of number 23 ends with:

• 3
• 1
• 9
• 4

Solution

Square of 23 ends with 9 as its unit's place is 3.

Q16. A number is called a triangular number if its dot pattern can be arranged in

• a triangle
• a triangle and a rectangle
• a rectangle
• a rectangle and a line

Solution

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

Q17. (n + 1)² - n² =

• 4n + 1
• 2n + 1
• 2n - 1
• 2n

Solution

(n + 1)² - n² = n² + 2n + 1 - n² = 2n + 1

Q18. The least square number which is greater than 140 is:

• 225
• 169
• 144
• 150

Solution

We know that 140 lies between the square numbers 121 and 144.Thus, the least square number which is greater than 140 is 144.

Q19. Number of zeros in the square of 4000 is :

• 4
• 3
• 6
• 10

Solution

Since 4000 has 3 zeros, its square will have 6 zeros.

Q20. Square of number 23 ends with:

• 3
• 1
• 9
• 4

Solution

Square of 23 ends with 9 as its unit's place is 3.

Q21. (589)² = (250 + 89) x 1000 + ________

• (8 + 9)²
• (89)²
• (8² x 9²)
• (89)

Solution

(589)² = (250 + 89) x 1000 + (89)²

Q22. Area of a square sheet is 300 cm². The nearest whole number to which its side can be estimated is

• 15
• 16
• 17
• 18

Solution

Area of the square sheet = 300 m²Length of the side of the square sheet = Now, we know that 289 < 300 < 324Also, 17² = 289 and 18² = 324. And, 300 is nearer to 289 than 324.Therefore, the whole number which is nearest to the side length of the square sheet, that is, is 17.

Q23. Using property of square numbers, the value of 15 x 17 is:

• 15² - 1
• 16² - 1
• 17² - 1
• 22² - 1

Solution

We know that: (a + 1)(a - 1) = a² - 1 15 x 17 = (16 - 1)(16 + 1) = 16² - 1

Q24. A gardener has to plant 500 saplings in such a way that number of rows and number of saplings in each row are the same. How many saplings would be left out?

• 18
• 16
• 24
• 25

Solution

Q25. Observe the following pattern: 72 = 49 672 = 4489 6672 = 444889 66672= 44448889 Using the given pattern, we have 666672= 

• 444488889
• 4444488899
• 444448889
• 4444488889

Solution

Following the pattern, we have: 666672= 4444488889

Q26. Which of the following is not a triangular number?

• 3
• 6
• 10
• 11

Solution

11 is not a triangular number.

Q27. Which of the following numbers is a square as well as a triangular number?

• 1
• 6
• 10
• 28

Solution

1 is a square as well as a triangular number.

Q28. The square of the number 59 can be written as

• 60 + 2 x 60 x 1 + 1²
• 60 – 2 x 60 x 1 + 1²
• 60² + 2 x 60 x 1 + 1²
• 60² – 2 x 60 x 1 + 1²

Solution

59 = 60 - 159² = (60 - 1)² = 60² - 2 x 60 x 1 + 1²

Q29. A perfect square can be expressed as sum of successive ______ numbers starting from 1.

• odd
• even
• prime
• natural

Solution

odd

Q30. If the area of a square plot is 3249 sq m, then the perimeter of the plot is

• 238 m
• 228 m
• 208 m
• 224 m

Solution

Q31. The product of two numbers is 1296. If one number is 16 times the other, then the two numbers are

• 9 and 12
• 9 and 144
• 12 and 16
• 12 and 108

Solution

Given, one number is 16 times the other.Let the numbers be x and 16x.(x)(16x) = 129616x² = 1296x² = 81 = 3 x 3 x 3 x 3 x = 3 x 3 = 9Thus, the two numbers are 9 and 16 x 9 = 144.

Q32. Rahul deposited Rs.30 each day in his piggy bank for 30 consecutive days. The total amount in his piggy bank after 30 days is

• Rs.2 x 30
• Rs.30 + 30
• Rs.302
• Rs.4 x 30

Solution

Number of days = 30 Amount deposited every day = Rs 30 Total amount at the end of 30 days = Rs.302

Q33. The square root of a number whose prime factorisation is 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 is:

• 80
• 45
• 90
• 180

Solution

Square root of a number with prime factorisation 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 = 2 x 3² x 5 = 2 x 9 x 5 = 90

Q34. By diagonal method, square of number 64 can be calculated by drawing a square and dividing it into

• 8 sub-squares
• 4 sub-squares
• 2 sub-squares
• 6 sub-squares

Solution

Number of digits in 64 = 2 Thus, sub-squares = 2² = 4

Q35. Using the pattern, 2²= 4 20²= 400 We get 2000² =

• 40000
• 4000000
• 400000
• 40000000

Solution

Using the given pattern, 20002= 4000000

Q36. Which number should be subtracted from 150 to make it perfect square?

• 5
• 4
• 6
• 3

Solution

Remainder = 6 Thus, when 6 is subtracted from 150 we get a perfect square number. And, the perfect square number is 150 - 6 = 144.

Q37. If the square root of 49 is 7, then the square root of 490000 is:

• 70000
• 7000
• 700
• 70

Solution

490000 = 7 x 7 x 10 x 10 x 10 x 10 Square root of 490000 = 7 x 10 x 10 = 700.

Q38. There are ______ perfect squares less than 100.

• 6
• 7
• 8
• 9

Solution

There are 9 perfect squares less than 100. These perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81.

Q39. The product 19 x 21 can be expressed as:

• 18² - 1
• 19² - 1
• 20² - 1
• 21² - 1

Solution

We know that (a + 1) x (a - 1) = a² - 1 19 x 21 = (20 - 1)(20 + 1) = 20² - 1

Q40. The sum 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 is:

• 7²
• 8²
• 9²
• 10²

Solution

We know that the sum of first n odd natural numbers is n². Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 92

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• 27
Q1. What is the square of 508?
• 317564
• 358064
• 258064
• 250864

Solution

Q2. 205² can be found by visual method taking a and b as _______ and _______.

• 20, 5
• 2, 5
• 200, 5
• 25, 5

Solution

205² = 200 + 5 Thus, a = 200 and b = 5

Q3. Estimated value of the square root of 10 to the nearest whole number is

• 3
• 4
• 5
• 6

Solution

Q4. If the sides of a rectangle are 25 cm and 16 cm then the side of a square whose area is equal to the area of this rectangle is:

• 40 cm
• 30 cm
• 4 cm
• 20 cm

Solution

Area of square = Area of rectangle = 25 x 16 cm2 = 400 cm2 400 = 2 x 2 x 2 x 2 x 5 x 5 Side of the square = 2 x 2 x 5 = 20 cm

Q5. A number has 4 zeroes at the end. How many zeroes will its square have?

• 8
• 16
• 2
• 4

Solution

If a natural number has n zeroes at the end, its square have 2n zeroes at the end. So, the square of the number with 4 zeroes at the end will have 8 zeroes at the end.

Q6. By which number, should 588 be multiplied so as to get a perfect square?

• 2
• 3
• 5
• 7

Solution

We have: 588 = 2 x 2 x 3 x 7 x 7 As the prime factor 3 has no pair, 588 is not a perfect square. If 3 gets a pair, then the number will become a perfect square. Therefore, 588 has to be multiplied with 3 to obtain a perfect square. Therefore, 588 x 3 = 1764 is a perfect square.

Q7. Square root of 10.24 is:

• 0.32
• 3.2
• 3.02
• 3.002

Solution

  Square root of 10.24 is 3.2.

Q8. Which of the following is not a triangular number?

• 3
• 6
• 10
• 11

Solution

11 is not a triangular number.

Q9. Which of the following is a triangular number?

• 0
• 1
• 2
• -1

Solution

1 is a triangular number.

Q10. If a number has 1 or 9 in the unit's place, then it's square ends in

• 1
• 3
• 8
• 9

Solution

If a number has 1 or 9 in the unit's place, then it's square ends in 1.

Q11. The square root of 123454321 is ______ .

• 111111
• 111
• 1111
• 11111

Solution

Observe the following pattern: 1² = 1 11² = 121 111² = 12321 1111² = 1234321 11111² = 123454321 Thus, the square root of 123454321 is 11111.

Q12. The sum of first 5 consecutive odd numbers is:

• 16
• 18
• 25
• 36

Solution

We know that the sum of first n odd natural numbers is n². Thus, sum of first 5 consecutive odd numbers = 5²= 25.

Q13. The whole number whose square is nearer to the number 140 is:

• 11
• 12
• 13
• 14

Solution

We have: 121 < 140 < 144 Also, 112= 121 and 122= 144 Clearly, 140 is closer to 144 than 121.Thus, the required whole number whose square is nearer to the number 140 is 12.

Q14. The square of the number 65 is

• 3175
• 4215
• 3225
• 4225

Solution

Q15. Square of number 23 ends with:

• 3
• 1
• 9
• 4

Solution

Square of 23 ends with 9 as its unit's place is 3.

Q16. A number is called a triangular number if its dot pattern can be arranged in

• a triangle
• a triangle and a rectangle
• a rectangle
• a rectangle and a line

Solution

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

Q17. (n + 1)² - n² =

• 4n + 1
• 2n + 1
• 2n - 1
• 2n

Solution

(n + 1)² - n² = n² + 2n + 1 - n² = 2n + 1

Q18. The least square number which is greater than 140 is:

• 225
• 169
• 144
• 150

Solution

We know that 140 lies between the square numbers 121 and 144.Thus, the least square number which is greater than 140 is 144.

Q19. Number of zeros in the square of 4000 is :

• 4
• 3
• 6
• 10

Solution

Since 4000 has 3 zeros, its square will have 6 zeros.

Q20. Square of number 23 ends with:

• 3
• 1
• 9
• 4

Solution

Square of 23 ends with 9 as its unit's place is 3.

Q21. (589)² = (250 + 89) x 1000 + ________

• (8 + 9)²
• (89)²
• (8² x 9²)
• (89)

Solution

(589)² = (250 + 89) x 1000 + (89)²

Q22. Area of a square sheet is 300 cm². The nearest whole number to which its side can be estimated is

• 15
• 16
• 17
• 18

Solution

Area of the square sheet = 300 m²Length of the side of the square sheet = Now, we know that 289 < 300 < 324Also, 17² = 289 and 18² = 324. And, 300 is nearer to 289 than 324.Therefore, the whole number which is nearest to the side length of the square sheet, that is, is 17.

Q23. Using property of square numbers, the value of 15 x 17 is:

• 15² - 1
• 16² - 1
• 17² - 1
• 22² - 1

Solution

We know that: (a + 1)(a - 1) = a² - 1 15 x 17 = (16 - 1)(16 + 1) = 16² - 1

Q24. A gardener has to plant 500 saplings in such a way that number of rows and number of saplings in each row are the same. How many saplings would be left out?

• 18
• 16
• 24
• 25

Solution

Q25. Observe the following pattern: 72 = 49 672 = 4489 6672 = 444889 66672= 44448889 Using the given pattern, we have 666672= 

• 444488889
• 4444488899
• 444448889
• 4444488889

Solution

Following the pattern, we have: 666672= 4444488889

Q26. Which of the following is not a triangular number?

• 3
• 6
• 10
• 11

Solution

11 is not a triangular number.

Q27. Which of the following numbers is a square as well as a triangular number?

• 1
• 6
• 10
• 28

Solution

1 is a square as well as a triangular number.

Q28. The square of the number 59 can be written as

• 60 + 2 x 60 x 1 + 1²
• 60 – 2 x 60 x 1 + 1²
• 60² + 2 x 60 x 1 + 1²
• 60² – 2 x 60 x 1 + 1²

Solution

59 = 60 - 159² = (60 - 1)² = 60² - 2 x 60 x 1 + 1²

Q29. A perfect square can be expressed as sum of successive ______ numbers starting from 1.

• odd
• even
• prime
• natural

Solution

odd

Q30. If the area of a square plot is 3249 sq m, then the perimeter of the plot is

• 238 m
• 228 m
• 208 m
• 224 m

Solution

Q31. The product of two numbers is 1296. If one number is 16 times the other, then the two numbers are

• 9 and 12
• 9 and 144
• 12 and 16
• 12 and 108

Solution

Given, one number is 16 times the other.Let the numbers be x and 16x.(x)(16x) = 129616x² = 1296x² = 81 = 3 x 3 x 3 x 3 x = 3 x 3 = 9Thus, the two numbers are 9 and 16 x 9 = 144.

Q32. Rahul deposited Rs.30 each day in his piggy bank for 30 consecutive days. The total amount in his piggy bank after 30 days is

• Rs.2 x 30
• Rs.30 + 30
• Rs.302
• Rs.4 x 30

Solution

Number of days = 30 Amount deposited every day = Rs 30 Total amount at the end of 30 days = Rs.302

Q33. The square root of a number whose prime factorisation is 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 is:

• 80
• 45
• 90
• 180

Solution

Square root of a number with prime factorisation 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 = 2 x 3² x 5 = 2 x 9 x 5 = 90

Q34. By diagonal method, square of number 64 can be calculated by drawing a square and dividing it into

• 8 sub-squares
• 4 sub-squares
• 2 sub-squares
• 6 sub-squares

Solution

Number of digits in 64 = 2 Thus, sub-squares = 2² = 4

Q35. Using the pattern, 2²= 4 20²= 400 We get 2000² =

• 40000
• 4000000
• 400000
• 40000000

Solution

Using the given pattern, 20002= 4000000

Q36. Which number should be subtracted from 150 to make it perfect square?

• 5
• 4
• 6
• 3

Solution

Remainder = 6 Thus, when 6 is subtracted from 150 we get a perfect square number. And, the perfect square number is 150 - 6 = 144.

Q37. If the square root of 49 is 7, then the square root of 490000 is:

• 70000
• 7000
• 700
• 70

Solution

490000 = 7 x 7 x 10 x 10 x 10 x 10 Square root of 490000 = 7 x 10 x 10 = 700.

Q38. There are ______ perfect squares less than 100.

• 6
• 7
• 8
• 9

Solution

There are 9 perfect squares less than 100. These perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81.

Q39. The product 19 x 21 can be expressed as:

• 18² - 1
• 19² - 1
• 20² - 1
• 21² - 1

Solution

We know that (a + 1) x (a - 1) = a² - 1 19 x 21 = (20 - 1)(20 + 1) = 20² - 1

Q40. The sum 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 is:

• 7²
• 8²
• 9²
• 10²