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Properties of Square NumbersCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! In this section we will discuss properties of square numbers.Property 1: A number having 2, 3, 7 or 8 at unit’s place is never a perfect square. In other words, no square number ends in 2, 3, 7 or 8. Example: None of the numbers 152, 7693, 14357, 88888, 798328 is a perfect square because the unit digit of each number ends with 2,3,7 or 8 Property 2: The number of zeros at the end of a perfect square is always even. In other words, a number ending in an odd number of zeros is never a perfect square. Example : 2500 is a perfect square as number of zeros are 2(even) and 25000 is not a perfect square as the number of zeros are 3 (odd). Property 3: Squares of even numbers are always even numbers and square of odd numbers are always odd. Example : 12 ^{2} = 12 x 12 = 144. (both are even numbers) 19 ^{2} = 19 x 19 = 361 (both are odd numbers) Property 4: The Square of a natural number other than one is either a multiple of 3 or exceeds a multiple of 3 by 1. In other words, a perfect square leaves remainder 0 or 1 on division by 3.
Example: 635,98,122 are not perfect squares as they leaves remainder 2 when divided by 3. Property 5: The Square of a natural number other than one is either a multiple of 4 or exceeds a multiple of 4 by 1. Example : 67,146,10003 are not perfect squares as they leave remainder 3,2,3 respectively when divided by 4. Property 6: The unit’s digit of the square of a natural number is the unit’s digit of the square of the digit at unit’s place of the given natural number. Example : 1) Unit digit of square of 146. Solution : Unit digit of 6 ^{2} = 36 and the unit digit of 36 is 6, so the unit digit of square of 146 is 6. 2) Unit digit of square of 321. Solution : Unit digit of 1 ^{2} = 1, so the unit digit of square of 321 is 1. Property 7: There are n natural numbers p and q such that p ^{2} = 2q ^{2} . Property 8: For every natural number n, (n + 1) ^{2}  n ^{2} = ( n + 1) + n. Properties of square numbers 9: The square of a number n is equal to the sum of first n odd natural numbers. 1 ^{2} = 1 2 ^{2} = 1 + 3 3 ^{2} = 1 + 3 + 5 4 ^{2} = 1 + 3 + 5 + 7 and so on. Properties of square numbers 10: For any natural number m greater than 1, (2m, m ^{2}  1, m ^{2} + 1) is a Pythagorean triplet. Squares and Square roots • Introduction of Squares and Square Roots • Perfect Squares or not • Properties of Square Numbers • Short cut method to find squares • Introduction of Square Roots • Properties of Square Roots • Square root by Prime factorization method • Square root by long division method • Square root of rational numbers • Square root of Decimals • Square root by estimation method Home Page Covid19 has affected physical interactions between people. Don't let it affect your learning.
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