What will be the unit digit of the squares of the following numbers?

1. 81               

2. 272           

3. 799          

4. 3853             

5. 1234              

6. 26387

7. 52698   

8. 99880     

9. 12796       

10. 55555

The following numbers are obviously not perfect squares. Give reasons.

1. 1057                            

2. 23453                     

3. 7928                        

4. 222222

5. 64000                        

6. 89722                    

7. 222000                  

8. 505050

The squares of which of the following would be odd number:

1. 431               

2. 2826           

3. 7779           

4. 82004

Observe the following pattern and find the missing digits:

11² = 121

101² = 10201

1001² = 1002001

100001² = 1……2……...1

10000001² = 1……………….

Observe the following pattern and supply the missing numbers:

11² = 121

101² = 10201

10101² = 102030201

1010101² = ………………….

……………….² = 1020304050403020101

Using the given pattern, find the missing numbers:

1² + 2² + 2² = 3²

2² + 3² + 6² = 7²

3² + 4² + 12² = 13²

4² + 5² + __² = 21²

5² + __² + 30² = 31²

6² + 7² + __² = __²

Without adding, find the sum:

1. 1 + 3 + 5 + 7 + 9

2. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

3. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

1. Express 49 as the sum of 7 odd numbers.

2. Express 121 as the sum of 11 odd numbers.

How many numbers lie between squares of the following numbers:

1. 12 and 13                         

2. 25 and 26                     

3. 99 and 100

Find the squares of the following numbers:

1. 32              

2.  35           

3. 86           

4. 93           

5. 71             

6. 46

Write a Pythagoras triplet whose one member is:

1. 6                                 

2. 14                              

3. 16                                

4. 18

What could be the possible ‘one’s’ digits of the square root of each of the following numbers:

1. 9801                  

2. 99856                 

3. 998001                          

4. 657666025

Without doing any calculation, find the numbers which are surely not perfect squares:

1. 153                      

2. 257                     

3. 408                       

4. 441

Find the square roots of 100 and 169 by the method of repeated subtraction.

 

Find the square roots of the following numbers by the Prime Factorization method:

1. 729                    

2. 400               

3. 1764              

4. 4096              

5. 7744

6. 9604              

7. 5929           

8. 9216            

9. 529                 

10. 8100

For each of the following numbers, find the smallest whole number by which it should be

multiplied so as to get a perfect square number.

Also, find the square root of the square number so obtained:

1. 252        

2. 180       

3. 1008        

4. 2028        

5. 1458         

6. 768

For each of the following numbers, find the smallest whole number by which it should be multiplied so

as to get a perfect square number. Also, find the square root of the square number so obtained:

1. 252        

2. 180       

3. 1008        

4. 2028        

5. 1458         

6. 768

The students of Class VIII of a school donated ` 2401 in all, for Prime Minister’s National Relief Fund.

Each student donated as many rupees as the number of students in the class.

Find the number of students in the class.

2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows.

Find the number of rows and the number of plants in each row.

Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.

Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.

Find the square roots of each of the following numbers by Division method:

1. 2304          

2. 4489         

3. 3481         

4. 529           

5. 3249          

6. 1369

7. 5776      

8. 7921       

9. 576           

10. 1024          

11. 3136         

12. 900

Find the number of digits in the square root of each of the following numbers (without any calculation):

1. 64            

2. 144         

3. 4489         

4. 27225          

5. 390625

Find the square root of the following decimal numbers:

1. 2.56           

2. 7.29           

3. 51.84             

4. 42.25             

5. 31.36

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square.

Also, find the square root of the perfect square so obtained:

1. 402          

2. 1989           

3. 3250          

4. 825            

5. 4000

Find the least number which must be added to each of the following numbers so as to get

a perfect square. Also, find the square root of the perfect square so obtained:

1. 525              

2. 1750             

3. 252              

4. 1825                 

5. 6412

Find the length of the side of a square whose area is 441 m²?

In a right triangle ABC, ÐB = 90⁰.

1. If AB = 6 cm, BC = 8 cm, find AC.

2. If AC = 13 cm, BC = 5 cm, find AB.

A gardener has 1000 plants. He wants to plant these in such a way that the

number of rows and number of columns remain same.

Find the minimum number of plants he needs more for this.

 

There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number

of rows is equal to number of columns. How many children would be left out in this arrangement?