Question

Find the least no. Of four digits that it is perfect square

Answer 1

Smallest 4-digit no. = 1,000

[ first of all we need to calculate the sq. root if 1,000 by long division method ]

[ then do as follows ]

The remainder = 39

sq. formed = 31²
Next perfect sq. = 32²

Clearly, (31)² < 1,000 < (32)²

Least no. which must be added
= 32² - 1000
= 1024 - 1000
= 24

Hence, the required no.
= (1000+24) = 1024

As,
$\sqrt{1024} = 32$

Answer 2

Step-by-step explanation:

Smallest 4-digit no. = 1,000

[ first of all we need to calculate the sq. root if 1,000 by long division method ]

[ then do as follows ]

The remainder = 39

sq. formed = 31²

Next perfect sq. = 32²

Clearly, (31)² < 1,000 < (32)²

Least no. which must be added

= 32² - 1000

= 1024 - 1000

= 24

Hence, the required no.

= (1000+24) = 1024

As,

√1024= 32