Question

Q.4. Also arrange these in such a manner that there are 2 digits in 1st row. It is to
be multiplied with a 3rd digit to get answer in a number of 4th and 5th (two)
digits. To the answer obtained we add a numbers 6th and 7th (two) digits
number to get a two digit number as answer made up of 8th and 9th digit.
Here also no digit is to be repeated.​

Answer 1

Answer:

1. 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.

2. The following numbers are obviously not perfect squares. Give reason.

(i) 1057(ii) 23453(iii) 7928(iv) 222222 (v) 64000(vi) 89722(vii) 222000(viii) 505050

Sol: (i) 1057

Since, the ending digit is 7 (which is not one of 0, 1, 4, 5, 6 or 9)

∴1057 is not a perfect square.

(ii) 23453

Since, the ending digit is 7 (which is not one of 0, 1, 4, 5, 6 or 9).

∴23453 is not a perfect square.

(iii) 7928

Since, the ending digit is 8 (which is not one of 0, 1, 4, 5, 6 or 9).

∴7928 is not a perfect square.

(iv) 222222

Since, the ending digit is 2 (which is not one of 0, 1, 4, 5, 6 or 9).

∴222222 is not a perfect square.

(v) 64000

Since, the number of zeros is odd.

∴64000 is not a perfect square.

(vi) 89722

Since, the ending digits is 2 (which is not one of 0, 1, 4, 5, 6 or 9).

∴89722 is not a perfect square.

(viii) 222000

Since, the number of zeros is odd.

∴222000 is not a perfect square.

(viii) 505050

The unit’s digit is odd zero.

∴505050 can not be a perfect square.