Worksheet - Properties of Square Numbers

Transcript

Worksheet - Properties of Square Numbers Let’s try solving these Questions Question 1 If a number contains 3 zeros at the end, how many zeros will its square have at the end? Question 2 What can you say about the parity of a number and its square? Question 3 Which of the following numbers have the digit 6 in the units place? (i) 382 (ii) 342 (iii) 462 (iv) 562 (v) 742 (vi) 822 Question 4 Write 5 numbers such that you can determine by looking at their units digit that they are not squares. Question 5 What will be the unit digit of the squares of the following numbers? (i) 52698 (ii) 99880 (iii) 55555 Question 6 The following numbers are obviously not perfect squares. Give reason. (i) 1057 (ii) 23453 (iii) 505050 Let’s answer one by one Zeroes of its square will double. So, Zeroes of square = 2 × 3 = 6 Question 2 What can you say about the parity of a number and its square?Parity means odd or even And, we know that Square of even numbers are always even, Square of odd numbers are always odd Question 3 Which of the following numbers have the digit 6 in the units place? (i) 382 (ii) 342 (iii) 462 (iv) 562 (v) 742 (vi) 822We know that If a number's last digit is 4 or 6, its square will end in 6. Thus, (ii) 342 , (iii) 462 , (iv) 562 , (v) 742 will have digit 6 in units place Question 4 Write 5 numbers such that you can determine by looking at their units digit that they are not squares.We know that Perfect squares never end in 2, 3, 7, or 8, and perfect squares do not have odd number of zeroes Thus, five required numbers can be 32 43 57 68 100,000 Question 5 What will be the unit digit of the squares of the following numbers? (i) 52698Unit digit of 526982 = Unit digit of 82 = Unit digit of 64 = 4 ∴ Unit digit of square of 52698 = 4 Question 5 What will be the unit digit of the squares of the following numbers? (ii) 99880Unit digit of 998802 = Unit digit of 02 = Unit digit of 0 = 0 ∴ Unit digit of square of 99880 = 0 Question 5 What will be the unit digit of the squares of the following numbers? (iii) 55555Unit digit of 555552 = Unit digit of 52 = Unit digit of 25 = 5 ∴ Unit digit of square of 55555 = 5 Question 6 The following numbers are obviously not perfect squares. Give reason. (i) 1057 We know that Perfect squares never end in 2, 3, 7, or 8, and perfect squares do not have odd number of zeroes Since 1057 ends with 7 ∴ 1057 is not a perfect square. Question 6 The following numbers are obviously not perfect squares. Give reason. (ii) 23453 We know that Perfect squares never end in 2, 3, 7, or 8, and perfect squares do not have odd number of zeroes Since 23453 ends with 3 ∴ It is not a perfect square. Question 6 The following numbers are obviously not perfect squares. Give reason. (iii) 505050 We know that Perfect squares never end in 2, 3, 7, or 8, and perfect squares do not have odd number of zeroes Since 505050 has 1 zero at the end, i.e. odd zeros ∴ It is not a perfect square.