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Question
What will be the units digit of the square of the following number?
4583
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Solution
The units digit is affected only by the last digit of the number. Hence, we only need to examine the square of its last digit.
Its last digit is 3. Hence, the units digit is 32, which is equal to 9.
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Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
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\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :
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