Question

what will be theunit digit of area of the square whose side is (10a+1) unit where a is any natural number​

Answer 1

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 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 the square of number 3853 is equal to 9.

v. The unit digit of the square of a number having digit 4 as unit’s place is 6.

∴ Unit digit of the square of number 1234 is equal to 6.

vi. The unit digit of the square of a number having digit 7 as unit’s place is 9.

∴ Unit digit of the square of number 26387 is equal to 9.

vii. The unit digit of the square of a number having digit 8 as unit’s place is 4.

∴ Unit digit of the square of number 52698 is equal to 4.

viii. The unit digit of the square of a number having digit 0 as unit’s place is 01.

∴ Unit digit of the square of number 99880 is equal to 0.

ix. The unit digit of the square of a number having digit 6 as unit’s place is 6.

∴ Unit digit of the square of number 12796 is equal to 6.

x. The unit digit of the square of a number having digit 5 as unit’s place is 5.

∴ Unit digit of the square of number 55555 is equal to 5.

Answer 2

Concept Introduction:

Having four equal edges and four equal angles, a square is a symmetrical quadrilateral. It is also known as a rectangular one with two neighboring sides of identical length.

Given, that the square whose side is ( $10a + 1$ ) unit

To find, the unit digit of the area of the square

Solution:

Let, a = $1$

Side = ( $10a + 1$ ) = $11$ unit

Area = $11$ × $11$ = $121$ unit²

Final Answer:

The final answer is $121$ unit²

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