Question

What will be the unit digit of the squares of the following numbers? 

1. 81 
2. 272 
3.  799 
4.  3853 
5.  1234 
6.  26387 
7.  52698 
8.  99880 
9.  12796
10.  55555

Answer 1

We know that if a number has its unit's place digit as a, then its square will end with the unit digit of the multiplication \(a \times a\).
(i) \(81\)
Since the given number has its unit's place digit as 1, its square will end with the unit digit of the multiplication \((1 \times 1 = 1)\) i.e., \(1\).

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(ii) \(272\)
Since the given number has its unit's place digit as \(2\), its square will end with the unit digit of the multiplication \((2 \times 2 = 4)\) i.e., \(4\).

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(iii) \(799\)
Since the given number has its unit's place digit as \(9\), its square will end with the unit digit of the multiplication \((9 \times 9 = 81)\) i.e., \(1\).

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(iv) \(3853\)
Since the given number has its unit's place digit as \(3\), its square will end with the unit digit of the multiplication \((3 \times 3 = 9)\) i.e., \(9\).

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(v) \(1234\) 
Since the given number has its unit's place digit as \(4\), its square will end with the unit digit of the multiplication \((4 \times 4 = 16)\) i.e., \(6\).

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(vi) \(26387\)
Since the given number has its unit's place digit as \(7\), its square will end with the unit digit of the multiplication \((7 \times 7 = 49)\) i.e., \(9\).

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(vii) \(52698\)
Since the given number has its unit's place digit as \(8\), its square will end with the unit digit of the multiplication \((8 \times 8 = 64)\) i.e., \(4\).

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(viii) \(99880\)
Since the given number has its unit's place digit as \(0\), its square will have two zeroes at the end.
Therefore, the unit digit of the square of the given number is \(0\).

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(xi) \(12796\)
Since the given number has its unit's place digit as \(6\), its square will end with the unit digit of the multiplication \((6 \times 6 = 36)\) i.e., \(6\).

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(x) \(55555\)
Since the given number has its unit's place digit as \(5\), its square will end with the unit digit of the multiplication \((5 \times 5 = 25)\) i.e., \(5\).