Question

Find the smallest number which must be subtracted
er which must be subtracted from
following numbers so as to get a perfect square number:
each of the
(11 1158
(2)2119
(3) 5480​

Answer 1

Step-by-step explanation:

1)10 is subtracted

2)3 is subtracted

3) 4 is subtracted

Answer 2

(1) 2 must be subtracted from 1158 to make it perfect square that is 1156.

(2) 3 must be subtracted from 2119 to make it perfect square that is 2116.

(3) 4 must be subtracted from 5480 to make it perfect square that is 5476.

Solution:

We need to find what number must be subtracted from each of following number to get perfect square number

(1) 1158:

Square of 34 = 34 x 34 = 1156

Square of 35 = 35 x 35 = 1225

Clearly position of the given number is between squares of 34 and 35

That is 1156< 1158< 1225

So if we subtract 2 from 1158, it will become 1156 which is perfect square of 34.

Hence 2 must be subtracted from 1158 to make it perfect square that is 1156

(2) 2119:

Square of 46 = 46 x 46 = 2116

Square of 47 = 47 x 47 = 2209

Clearly position of the given number is between squares of 46 and 47

That is 2116 < 2119 < 2209

So if we subtract 3 from 2119, it will become 2116 which is perfect square of 46.

Hence 3 must be subtracted from 2119 to make it perfect square that is 2116.

(3) 5480:

Square of 74 = 74 x 74 = 5476

Square of 75 = 75 x 75 = 5625

Clearly position of the given number is between squares of 74 and 75

That is 5476< 5480< 5625

So if we subtract 4 from 5480, it will become 5476 which is perfect square of 74.

Hence 4 must be subtracted from 5480 to make it perfect square that is 5476.