Question

(1) What will be the digits in the unit place of the squares of the following
RSION
numbers?
Excersie R-2
(m) 79
(iv) 2637
(iv) 640
0 272
(2) Why do the following numbers are not perfect square?
(m) 400
(1) 1057
(ii) 7928
(m) 222
(3) What are the squares of the following numbers?
() 19
( 37
(m) 53 (iv) 78
(4) Find the square roots of the following by prime factorisation method.
(1) 1764 (m) 9216
(i) 7744 (iv) 9801
(5) Find the least numbers (integer) with which the following numbers are
to be multiplied so that they become perfect squares.
(1) 1525 (1) 1008
(11) 2028 (iv) 768
(6) With what least numbers (integer) the following numbers are to be divided so
that they become perfect squares.
(1) 468
(i) 1584
(ii) 2645 (iv) 1620
(7) In a military camn th​

Answer 1

Answer:

1) To know the digits in the unit place of the square of a number, simply

take unit digit - in 79 , 9 is in unit digits place

so square of 9=9*9=81..

in 81 ...1 will be the digit in unit place of the sqaure of number 79

2)2637....7*7=49. ..=> 9 is digit in units place

3)640... clearly 0 would be in units place

4)272.......2*2=4 , 4 would be in units place

Why do the following numbers are not perfect squares?

=> square numbers end with 0, 1, 4, 5, 6 or 9. ...

a) 400...this number ends with 0 ,hence it is a perfect square

b) 1057.....this number doesnt meet the above criteria... where a sq num shud end with 0,1,4,5,6,9...hence it is nt a perfect square

c) 7928...this is not a perfect square

d) 222...this is not a perfect square

squares of the following

.19 -361

37-1369

53-2809

78- 6084

square roots of the following by prime factorization

1764 - 2*2*7*3*7*3

9216 - 2*2*2*2*2*2*2*2*2*2*3*3

7744 - 2*2*2*2*2*2*11*11

9801- 3*3*3*3*11*11

least numbers to be multiplied so that they become perfect square

a) 1525 - 5*305

5*5*61 ....remaining number is 61 ..so multiply 1525 with 61 ....1525*61 = 93205

square root of 93205 is 305

b) 1008 - 2* 504

2*2*252

2*2*2*126

2*2*2*2*63

2*2*,2*2*3*21

2*2*2*2*3*3*7 since 7 is remaining multiply 1008 with 7....1008*7 =7056...sq root of 7056 is 84

c) 2028 - 2*1014

2* 2*507

2*2*3*169

2*2*3*13*13....since 3 is single without a pair ... multiply 2028 with 3 ..2028*3=6084 sq root is 78

d) 768 - 2*384

2*2*192

2*2*2*96

2*2*2*2*48

2*2*2*2*2*24

2*2*2*2*2*2*12

2*2*2*2*2*2*2*6

2*2*2*2*2*2*2*2*3...since 3 is left... multiply 768*3=2304 => sq root is 48

least numbers the following numbers are to be divided for perfect square

1) 468 - 2*234

2*2*117

2*2*3*39

2*2*3*3*13

since 13 is left without a pair divide 468/13...answer =36...sq is 6

(i) 1584 - 2*2*2*2*3*3*11 ...

11 is left out, divide 1584/11 => 144 sq root is 12

(ii) 2645 -5 *23*23 ....since 5 is leftout, divide

2645/5 ==529 sq root is 23

(iv) 1620 = 2*2*3*3*3*3*5...5 is left out divide with 5

1620/5 = 324....sq root is 18