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NCERT Class 8 Mathematics Chapter 6 Square and Square Roots CBSE Board Sample Problems
Square and Square Roots
Square Number
If a natural number m can be expressed an where n is also a natural number, then m is a Square number
Some important point to note
S. no | Points |
1. | All Square numbers end with 0, 1,4, 5,6 or 9 at unit՚s place |
2. | If a number has 1 or 9 in unit՚s place, then it՚s Square ends in 1 |
3. | When a Square number ends in 6 the number whose Square it is, will have either 4 or 6 in unit՚s place |
4. | None of Square number with 2,3, 7 or 8 at unit՚s place |
5. | Even number square is even while odd number square is Odd |
6. | There are 2 n non perfect square numbers between the squares of the numbers n and (n + 1) |
7. | If a natural number cannot be expressed as a sum of successive odd natural numbers starting with 1 , then it is not a perfect square |
How to Find the Square of Number Easily
Sr. no | Method | Working |
1. | Identity method | We know that Example |
2. | Special cases | hundred + 25 Example |
Pythagorean Triplets
For any natural number , we have
So, 2 m, forms a Pythagorean triplet
Example
6,8, 10
Square Root
Square Root of a number is the number whose Square is given number
So we know that
Square root of m
Square root is denoted by expression
How to Find Square Root
Name | Description |
Finding Square root through repeated subtraction | We know sum of the first n odd natural numbers is . So in this method we subtract the odd number starting from 1 until we get the reminder as zero. The count of odd number will be the Square root Consider 36 Then. So 6 odd number, Square root is 6 |
Finding Square root through prime factorisation | This method, we find the prime factorization of the number. We will get same prime number occurring in pair for perfect Square number. Square root will be given by multiplication of prime factor occurring in pair Consider 81 |
Finding Square root by division method | This can be well explained with the example
In case of Decimal number, we count the bar on the integer part in the same manner as we did above, but for the decimal part, we start pairing the digit from first decimal part. |