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:
- Take the tens digit (the number before 5).
- Multiply that tens digit by the next higher number.
- 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:
- A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
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:
- A composite number is a natural number greater than 1 that has more than two distinct divisors.
- 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