Chapter 6 Q.1 Is 225 a perfect square? If so, find the number whose square is 225. Q2.Show that 63504 is a perfect square. Also, find the number whose square is 63504. Q3.Show that 17640 is not a perfect square? Q4. Find the smallest number by which 180 must be multiplied so that the product is a perfect square. Q5. Find the smallest number by which 25200 should be divided so that result is a perfect square. Q6. The following numbers are not perfect square. Give reason. a) 1057 b)23453 c)7928 d)222222 Q7. What will be the unit s digit of the squares of the following numbers? 1) 71 2)599 3)2783 4)1234 Q8. Which of the following end with digit 1? 123 2, 77 2, 82 2, 161 2, 109 2 Q9.Determine whether squares of the following number are even or odd. 1) 213 2) 3824 3)9777 4)40028 Q10. The following number are not perfect squares. Give reason. 1) 64000 2)89722 3)222000 4)505050 Q11.write a Pythagorean triplet whose one number is 1) 14 2)16 Q12 Without adding, find the sum a) 1+3+5+7+9 b)1+3+5+7+9+11+13+15+17+19 c) 1+3+5+7+9+11+13+15+17+19+21+23 Page 1
Q13. Express 1) 49 as the sum of 7 odd natural numbers 2) 121 as the sum of 11 odd natural nembers. Q14. How many natual numbers lie between squares of the following natural numbers? 1) 12 and 13 2)25 and 26 3)89and 100 Q15.Express each of the following as the sum of two consecutive natural numbers. 1) 12 2 2)13 2 3)19 2 Q16.find whether 55 is a perfect square or not? Q17. Observe the following pattern and find the missing digits 11 2 =121 101 2 =10201 1001 2 =1002001 10001 2 =100020001 100001 2 =1.2 1 10000001 2 =.. Q18.Observe the following pattern and supply the missing number 11 2 =121 101 2 =10201 10101 2 =102030201 1010101 2 =. =10203040504030201 Page 2
Q.19 Using the given pattern, find the missing numbers: 1 2 +2 2 +2 2 =3 2 2 2 +3 2 +6 2 =7 2 3 2 +4 2 +12 2 =13 2 4 2 +5 2 +( ) 2 =21 2 1 2 +2 2 +2 2 =3 2 5 2 +( ) 2 +30 2 =31 2 6 2 +7 2 +(_) 2 =( ) 2 Q.20 Using the suitable patterns, compute the following 1) 2) Part II Q1. Find the square of 87 by using column method and diagonal method. Q2.find the square of the following number by diagonal method. 1) 854 2) 2576 Q3. Find the squares of the following numbers: 1) 35 2) 105 3) 2005 Q4. Find the square of the following numbers 1) 515 2) 580 3) 509 Q5. Find the square of the following numbers using the identity. ( ) 1) 509 2)211 3) 625 Page 3
Q6. Find the square of the following numbers using the identity ( ) 1) 491 2)189 3)575 Q7. Find the square root of 11025 by prime factorization. Q8. Find the square root of 7744 by prime factorization. Q9. Find the square root of 298116 by prime factorization. Q10.find the smallest number by which 1100 must be multiplied so that product becomes a perfect square. Also, in each case find the square root of the perfect square so obtained. Q11. Find the smallest number by which 9408 must be divided so that it becomes a perfect square. Also, find the square root of the perfect square so obtained. Q12. 5929 students are sitting in an auditorium in such a manner that there areas many students in a row as there are rows in the auditorium. How many rows are there in the auditorium? Q13. A general wishing to arrange his men, who were335250 in number in the form of a square found that there were 9 men left over. How many were there in each row? Q14. The product of two number is 1575 and their quotient is Find the number. Q15. Find the smallest square number divisible by each one of the numbers 8,9,and 10. Q16. Find the square root of each of the following numbers by long division method 1) 54756 2)390625 3)4937284 Q17. Find the least number which must be subtracted from 18265 to make it a perfect square. Also, find the square root of the resulting number. Q18. Find the least number which must be added to 306452 to make it a perfect square. Q20. Find the greatest number of six digits which is a perfect square. Q21. Find the least number of four digits which is a perfect square. Q22. Find the square root of Page 4
Q23. Find the square root of Q24.find the square root of Q25. The area of a square field is square meter. Find the length of one side of the field. Q26. Find the value of 1) 2) 3) 4) Q27. Find the value of 1) 2) Q28. Find the square root of 477.4225 Q29. Find the square root of 0.00008281 Q30. Find the square root of 0.053361 Q31. A decimal fraction is multiplied by itself. If the product is 251953.8025, find the fraction. Q32. Find the value of and the use it to find the value of + Q33. Find the square root of 2304 and 1764 and hence find the value of Q34.find the square root of 3 correct to three places of decimal Q35. Find the square root of 237.615 correct to three places of decimal Page 5