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Squares And Square Roots

Question
CBSEENMA8002454

What will be the unit digit of the squares of the following numbers?

(i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555

Solution

(i) ∵ 1 × 1 = 1

 ∴ The unit’s digit of (81 )2 will be 1.

(ii) ∵ 2 × 2 = 4

 ∴ The unit’s digits of (272)2 will be 4.

(iii) Since, 9 × 9 = 81

 ∴ The unit’s digit of (799)2 will be 1.

(iv) Since, 3 × 3 = 9

 ∴ The unit’s digit of (3853)2 will be 9.

(v) Since, 4 × 4= 16

 ∴ The unit’s digit of (1234)2 will be 6.

(vi) Since 7 × 7 = 49

 ∴ The unit’s digit of (26387)2 will be 9.

(vii) Since, 8 × 8 = 64

 ∴ The unit’s digit of (52698)2 will be 4.

(viii) Since 0 × 0 = 0

 ∴ The unit’s digit of (99880)2 will be 0.

(ix) Since 6 x 6 = 36

 ∴ The unit’s digit of (12796)2 will be 6.

(x) Since, 5 x 5 = 25

 ∴ The unit’s digit of (55555)2 will be 5.