How many of the no. are perfect square.
a) 1057 b) 23453 C) 7928
Answers
Answer:
1.Therefore 1057 is not a perfect square because its unit's place digit is 7.
2. 23453 The number 23453 is not a perfect square because it ends with 3 whereas the square numbers end with 0, 1, 4, 5, 6 or 9.
3. Therefore 7928 is not a perfect square because its unit's place digit is 8.
How to find this type of questions :-
❑ The Squares of all integers are known as perfect squares. In this lesson, we will discuss a very interesting Mathematical shortcut: How to check whether a number is a perfect square or not. There are some properties of perfect squares which can be used to test if a number is a perfect square or not
❑ All perfect squares end in 1, 4, 5, 6, 9 or 00 (i.e. Even number of zeros). Therefore, a number that ends in 2, 3, 7 or 8 is not a perfect square.
❑ There are two types of numbers:
Numbers which are a perfect square: Product of an integer with itself. For example, 9*9 = 81.
Numbers which are an imperfect square: Multiplying any number with itself. For example, 2.236*2.236 = 5.
SOLUTION :
(a) Since, perfect square numbers contain their unit’s place digit 1, 4, 5, 6, 9 and even numbers of 0. Therefore 1057 is not a perfect square because its unit’s place digit is 7.
(b) Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9 and even number of 0. Therefore 23453 is not a perfect square because its unit’s place digit is 3.
(c) Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9 and even number of 0. Therefore 7928 is not a perfect square because its unit’s place digit is 8.