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What will be the units digit of the squares of the following numbers?
(i) 52
(ii) 977
(iii) 4583
(iv) 78367
(v) 52698
(vi) 99880
(vii) 12796
(viii) 55555
(ix) 53924.
To do:
We have to find the units digit of the squares of the given numbers.
Solution:
We know that,
The unit digit of square of a number having $a$ at its unit place will end with the units digit of $a \times a$.
(i) Here, the unit digit of the given number is 2.
This implies,
The units digit of the square of 52 $=2^2=4$.
The units digit of the square of the given number is $4$.
(ii) Here, the unit digit of the given number is 7.
This implies,
The square of the units digit of 977
$=7^2=49$.
Therefore,
The units digit of the square of the given number is $9$.
(iii) Here, the unit digit of the given number is 3.
This implies,
The square of the units digit of 4583
$=3^2=9$.
Therefore,
The units digit of the square of the given number is $9$.
(iv) Here, the unit digit of the given number is 7.
This implies,
The square of the units digit of 78367
$=7^2=49$.
Therefore,
The units digit of the square of the given number is $9$.
(v) Here, the unit digit of the given number is 8.
This implies,
The square of the units digit of 52698
$=8^2=64$.
Therefore,
The units digit of the square of the given number is $4$.
(vi) Here, the unit digit of the given number is 0.
This implies,
The square of the units digit of 99880
$=0^2=0$.
Therefore,
The units digit of the square of the given number is $0$.
(vii) Here, the unit digit of the given number is 6.
This implies,
The square of the units digit of 12796
$=6^2=36$.
Therefore,
The units digit of the square of the given number is $6$.
(viii) Here, the unit digit of the given number is 5.
This implies,
The square of the units digit of 55555
$=5^2=25$.
Therefore,
The units digit of the square of the given number is $5$.
(ix) Here, the unit digit of the given number is 4.
This implies,
The square of the units digit of 53924
$=4^2=16$.
Therefore,
The units digit of the square of the given number is $6$.
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