find the digit at unit place of cube of 5321
Answers
Answer:
Step-by-step explanation:
The last digit of 5321 is 1.
The cube of the last digit is = 1³ = 1
Therefore, the digit at the unit place of the cube of 5321 is 1.
Some other examples are:
A) 121
Unit digit of 121 is 1.
The digit at the unit's place of the cube is also 1.
B) 25
Unit digit of 25 is 5.
The digit at the unit's place of the cube is also 5.
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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