What will be the unit digit of product of square of first 9 natural numbers? * a.0 b.1 c.6 d.4
Answers
Answer:
The unit digit of square of a number having 'a' at its unit place ends with a×a. i. The unit digit of the square of a number having digit 1 as unit’s ... More
Step-by-step explanation:
The unit digit of square of a number having 'a' at its unit place ends with a×a.
i. The unit digit of the square of a number having digit 1 as unit’s place is 1.
∴ Unit digit of the square of number 81 is equal to 1.
ii. The unit digit of the square of a number having digit 2 as unit’s place is 4.
∴ Unit digit of the square of number 272 is equal to 4.
iii. The unit digit of the square of a number having digit 9 as unit’s place is 1.
∴ Unit digit of the square of number 799 is equal to 1.
iv. The unit digit of the square of a number having digit 3 as unit’s place is 9.
Unit Digit of Product of square of first 9 natural numbers is 0.
Given:
Product of square of first 9 natural numbers
To Find:
Unit digit
Solution:
Natural numbers are positive integers
Product of square of first 9 natural numbers is same as square of Product of first 9 natural numbers. (∵ ( a × b)² = (a² x b²) )
Step 1:
Product of First 9 natural number
1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9
Step 2:
First 9 natural number has 2 and 5 whose product is 10
(1 x 3 x 4 x 6 x 7 x 8 x 9) x 10
Step 3:
Product of any number multiplied with 10 , always have unit digit 0
Also Square of a number having unit digit 0 is always having unit digit 0
Hence, Unit digit of square of Product of first 9 natural numbers is 0
So, Unit digit of Product of square of first 9 natural numbers is 0
Unit Digit of Product of square of first 9 natural numbers is 0.