Properties of Square Roots




Properties of square roots

Property 1: If the units digit of a number is 2,3,7 or 8, then it does not have root in N (the set of natural numbers).
Example : 132, 433, 688 does not have perfect square roots as unit digits are 2,3,and 8 respectively.

Property 2: If a number ends in an odd number of zeros, then it does not have a square root. If a square number is followed by an even number of zeros, it has a square root in which the number of zeros in the end is half the number of zeros in the number.
Example : 2000 does not have prefect square root as the number of zeroes are 3(odd). 900 have a perfect square root as number of zeroes are 2(even). So square root of 900 will contain only 1 zero.(half of two zeroes).√900 = 30.

Property 3: The square root of an even square number is even and that root of an odd square number is odd.
Example : √144 = 12 (both are even numbers) and √225 = 15 (both are odd numbers).

Property 4: If a number has a square root in N, then its unit digit must be 0, 1, 4, 5, or 9.
Example : Unit digit of √1024 is 2 as unit digit of 1024 is 4 and its square root is 2.

Property 5: Negative numbers have no square root in the system of rational numbers.
Example : √(-9) is not a rational number. It will be complex number.

Property 6: The sum of first n odd numbers is n2.
Example :
1 + 3 + 5 = 9 = 32 as there are 3 odd numbers so it will be 32.
1 + 3 + 5 + 7 + 9 = 52 = 25 as there are 5 odd numbers.
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Practice on properties of Square Roots


Q.1 Write the possible unit digit of square root of :
1) 9801 2) 1156 3) 27225 (Answer)

Q.2 Find the sum of the following numbers without actually adding the numbers.
1) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
2) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 (Answer)
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

From squares and square roots to Exponents

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