# Properties of Square Roots

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**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 n

^{2}.

**Example :**

1 + 3 + 5 = 9 = 3

^{2}as there are 3 odd numbers so it will be 3

^{2}.

1 + 3 + 5 + 7 + 9 = 5

^{2}= 25 as there are 5 odd numbers.

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**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

• 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

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