18. Square any number ending in 5. Ex- 35, 65, 95, 105 etc


Maths :


Shortcut method of square any number ending in 5.  


The general formula is : (Tens digit) × (Tens digit + 1) and then add 25



Pattern for squaring numbers ending in 5:



  1. Take the tens digit (the number before 5).

  2. Multiply that tens digit by the next higher number.

  3. Append 25 at the end.


Ex 1: 25²



  • Tens digit = 2

  • Multiply 2 × 3 = 6

  • Add 25 at the end: 625


So, 25² = 625.


Ex 2: 35²



  • Tens digit = 3

  • Multiply 3 × 4 = 12

  • Add 25 at the end: 1225


So, 35² = 1225.


Ex 3: 45²



  • Tens digit = 4

  • Multiply 4 × 5 = 20

  • Add 25 at the end: 2025


So, 45² = 2025.


Ex 4: 85²



  • Tens digit = 8

  • Multiply 8 × 9 = 72

  • Add 25 at the end: 7225


So, 85² = 7225.


Ex 5: 95²



  • Tens digit = 9

  • Multiply 9 × 10 = 90

  • Add 25 at the end: 9025


So, 95² = 9025.


What is Prime Numbers & Composite Numbers ?


Prime Numbers:



  1. A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.


  2. Example: 2, 3, 5, 7, 11, 13, 17, 19, etc.



    • 2 is prime because its only divisors are 1 and 2.


    • 3 is prime because its only divisors are 1 and 3.






Composite Numbers:



  1.  A composite number is a natural number greater than 1 that has more than two distinct divisors.

  2.  In other words, composite numbers can be divided by numbers other than 1 and themselves.


Example: 4, 6, 8, 9, 10, 12, 15, etc.





    • 4 is composite because its divisors are 1, 2, and 4.

    • 6 is composite because its divisors are 1, 2, 3, and 6.




Summary:



  • Prime: Only 1 and the number itself are divisors.

  • Composite: Has more than two divisors.


For example:



  • Prime: 2, 3, 5, 7

  • Composite: 4, 6, 8, 9