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Wednesday, 4 November 2015

Square And Square Roots Practice Test paper

 Square And Square Roots Practice Test paper

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

(i) 81  (ii) 272  (iii) 799 (iv) 3853(v) 1234 
(vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555
[ hint:  52 = 25 So, 555552 will have 5 at unit’s place]

2. The following numbers are obviously not perfect squares. Give reason.

(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 
(v) 64000 (vi) 89722 (vii) 222000 (viii) 505050



[Numbers having only  0, 1, 4, 5, 6, and 9 at unit’s place and even 
number of zeroes at the end, are perfect squares.]


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

(i) 431 (ii) 2826 (iii) 7779 (iv) 82004

4. (i) Express 49 as the sum of 7 odd numbers.

     (ii) Express 121 as the sum of 11 odd numbers.

5. Without adding, find the sum.

(i) 1 + 3 + 5 + 7 + 9    (ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19
 (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

6. How many numbers lie between squares of the following numbers?
  (i) 12 and 13  (ii) 25 and 26   (iii) 99 and 100
[992 = 9801 , 1002 = 10000 ,Now, 10000 - 9801 = 199  So, there are 199 - 1 = 198 numbers lying between 992 and 1002 ]



7. Write a Pythagorean triplet whose one member is. (ii) 14  (iii) 16  (iv) 18
[ As we know 2m, m2+1 and m2-1 form a Pythagorean triplet for any number, m>1.]



8. What could be the possible ‘one’s’ digits of the square root of each of the following numbers?
(i) 9801 (ii) 657666025  (iii) 998001 (iv) 99856 [ 42 = 16 and 62 = 36, hence, 4 and 6 are possible]

9. 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.
(i) 252  (ii) 180  (iii) 1008  (iv) 2028  (v) 1458  (vi) 768 


10 . For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained.
(i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620


11. The students of Class VIII of a school donated Rs 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.


12. 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.

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

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


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

(i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625

[ If there are even number of digits in square then number of digits in square root = n/2
If there are odd number of digits in square then number of digits in  square root [n+1] /2 ]


16. Find the square root of the following decimal numbers.(i) 2.56 (ii) 7.29(iii) 51.84(iv) 42.25(v) 31.36


17. 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.         (i) 402  (ii) 1989  (iii) 3250  (iv) 825  (v) 4000


 18. 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.     (i) 525 (ii) 1750  (iii) 252  (iv) 1825  (v) 6412


19. A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.


20. 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.
                                                                       Cube and cube root Paper -2
1. Find the one.s digit of the cube of 3031

2. Without actually finding the cubes find the value of 21^3- 20^3

3. Is 32 a perfect cube?

4. Express 132 as the sum of two consecutive integers.

5. What will be the unit digit of the square of 3873?

6. Why 2332 is not perfect square ?

 7. Cube of any odd number is even. Yes/No Why?

8. Find the cube root of 27000.

9. Find the cube root of 17576 through estimation.

8. Anubhav makes a cuboid of plasticine of sides 5 cm, 3 cm, 5 cm. How many  such cuboids will he need to form a cube?

 9. Is 5488 a perfect cube? If not, find the smallest natural number by which 5488 must be multiplied so that the product is a perfect cube

10. Is 5324 a perfect cube? If not, then by which smallest natural number should   5324 be divided so that the quotient is a perfect cube?
Part 2

1. Find the square root of the following by means of factors   i) 529 2. ii) 298116 

2. Find the smallest number by which 252 must be multiplied to get a perfect  square. Also, find  the  quare root of the perfect square so obtained.  

4. Find the smallest number by which 2925 must be divided to get a perfect  square. Also, find the square root of the perfect square so obtained.  

5. Find the least square number, exactly divisible by each one of the numbers 6,  9, 15 and 20

6. Find the least square number exactly divisible by each one of the numbers 8,  12, 15, 20.  

7. Find the square root of:   (a)  9126441   (b) 63409369 

9. Find the least number that must be subtracted from 7581 to obtain a perfect  square. Find the perfect square and its square root.   

10. Find the least number that must be added to 506900 to make it a perfect  square. Find its perfect square and its square root.   

11. Find the least number of 4 digits that is a perfect square.  

12. The area of a square field is 60025 m 2. A man cycles around its boundary at  18 km per hour. In how much time will he return at the starting point?  

13. The sides of a rectangular field are 80 m and 18 m respectively. Find the length of its diagonal.  

14. Find the square root of  (a) 14. 10.0469 (b) 15. 0.00038809 

15. Find the value of the following up to three places of decimal:      

16. A decimal fraction is multiplied by itself to give the product 0.007569. Find  the decimal fraction.  

17. The area of a square playground is 291.0436 square meters. Find the length  of each side of the playground.  

18. Find the square root of:   (1)  25 +544/729     (ii)   21  + 2797/3364    (iii)    3 + 334/3025  

19. Find the square root of: (i)  √7/2

20. Find the value  of Sq.root under 103.0225 and hence write down the square root of   (i) Square root under 10302.25 (ii)  1.030225  

 21. Evaluate:         (i ) √72 x √338    (ii ) √ 45 x√20  (iii ) √147 x  √243    ·   

 22. The area of a square field is   80+244/729  square meters. Find the length of
each  side of the field




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