Question

show that the following numbers are not perfect square

Answer 1

2canot be aperfect square

Answer 2

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

Sol: (i) ∵ 1 × 1 = I

              ∴ 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.

         (v) Since, 8 × 8 = 64

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

         (vi) Since 0 × 0 = 0

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

         (vii) Since 6 × 6 = 36

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

         (x) Since, 5 × 5 = 25

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