### Square Root and Cube Root

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 X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
 X² 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 841 900 X³ 1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096 4913 5832 6859 8000 9261 10648 12167 13824 15625 17576 19683 21952 24389 27000

Finding the unit digit of given numbers:

Now let us observe the pattern in the cycle of different digit in other words after how many cycles the last digit repeats itself.

 2 3 4 5 6 7 8 9 21 = 2 31 = 3 41 = 4 51 = 5 61 = 6 71 = 7 81 = 8 91 = 9 22 = 4 32 = 9 42 = 6 52 = 5 62 = 6 72 = 9 82 = 4 92 = 1 23 = 8 33 = 7 43 = 4 53 = 5 63 = 6 73 = 3 83 = 2 93 = 9 24 = 6 34 = 1 44 = 6 54 = 5 64 = 6 74 = 1 84 = 6 94 = 1 25 = 2 35 = 3 45 = 4 55 = 5 65 = 6 75 =  7 85 = 8 95 = 9 26 = 4 36 = 9 46 =6 56 = 5 66 = 6 76 = 9 86 = 4 96 = 1 27 = 8 37 = 7 47 = 4 57= 5 67 =  6 77 = 3 87 = 8 97 = 9

from the above table we can conclude that

after each power that is either 4 or multiple of four the digits repeats themselves

Q 1) find the unit digit of 257

We know in case of 2, it repeats itself after a cycle of 4 . We will divide 57 by 4

57/4 remainder is 1

We write it as

257= 21= 2

That means the unit digit in the 257 is 2.

Q 2) find the unit digit of 388 ?

Solution:

88/4 the remainder is 0.

In such cases, our answer should be the 4th power

So answer is unit digit in 34is 1.

Q3)  find the unit digit of 7458000

Solution: In this case we need to divide the power by 4

The power is 458000

or 458000/4 = 0 remainder
74if you still find difficult, let us simplify it

74= 7× 72

= 9 × 9 (Unit digits)

81 Unit digit so the last digit in the 7458000is

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