? Find the digit at unit place of cube of 5321
Answers
Given : 5321³
To Find : Digit at unit Place
Solution:
0³ = 0 ends with 0
1³ = 1 ends with 1
2³ = 8 end with 8
3³ = 27 ends with 7
4³ = 64 ends with 4
5³ = 125 ends with 5
6³ = 216 ends with 6
7³ = 343 ends with 3
8³ = 512 ends with 2
9³ = 729 ends with 9
As 5321 ends with 1
Hence 5321³ ends with 1
unit place of cube of 5321 is 1
Another way
5321³
= (5320 + 1)³
using (a + b)³ = a³ + b³ + 3ab(a + b)
a = 5320
b = 1
= 5320³ + 1³ + 3(5320)(1)(5320 + 1)
= 10³ x 532³ + 10 x 3 x 532 (5321) + 1
= 10 x 100 x 532³ + 10 x 3 x 532 (5321) + 1
= 10 ( 100 x 532³ + 3 x 532 (5321) ) + 1
= 10k + 1
Hence Digit at unit place is 1
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