What will be the unit digit of the area of a square whose side is (10a+1) units, where a is any natural number?
Answers
Given : a square whose side is (10a+1) units, where a is any natural number
To Find : unit digit of the area of the square
Solution:
Area of a square = ( side )²
side is (10a+1) units
=> Area of the square = (10a + 1)² sq units
using (x + y)² = x² + 2xy + y²
x = 10a , y = 1
= (10a)² + 2(10a)(1) + 1²
= 100a² + 20a + 1
= 10(10a² + 2a) + 1
= 10k + 1 where k = 10a² + 2a
Hence unit digit is 1
unit digit of the area of a square whose side is (10a+1) units, where a is any natural number is 1
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Answer:
Area of a square = (side)²
side is (10a+1) units
=> Area of the square = (10a + 1)² sq units
using (x + y)² = x² + 2xy + y²
x = 10a y = 1
= (10a)² + 2(10a)(1) + 1²
= 100a² + 20a + 1
= 10(10a² + 2a) +1
where k = 10a² + 2a Hence unit digit is 1
= 10k + 1
unit digit of the area of a square whose side is (10a+1) units, where a is any natural number is 1.