Question

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square Also find the square root of the perfect square so obtained
$\left(i\right)402,\left(ii\right)1989,\left(iii\right)3250,\left(iv\right)825,\left(v\right)4000$

• A. Least number which must be subtracted:$\left(i\right)2,\left(ii\right)22,\left(iii\right)1,\left(iv\right)21,\left(v\right)52$
  Square root of the perfect square:
  $\left(i\right)20,\left(ii\right)34,\left(iii\right)55,\left(iv\right)26,\left(v\right)67$
  
• B. Least number which must be subtracted:$\left(i\right)2,\left(ii\right)53,\left(iii\right)1,\left(iv\right)41,\left(v\right)31$
  Square root of the perfect square:
  $\left(i\right)20,\left(ii\right)44,\left(iii\right)57,\left(iv\right)28,\left(v\right)63$
• C. Least number which must be subtracted:$\left(i\right)6,\left(ii\right)22,\left(iii\right)50,\left(iv\right)31,\left(v\right)40$
  Square root of the perfect square:
  $\left(i\right)19,\left(ii\right)41,\left(iii\right)49,\left(iv\right)27,\left(v\right)65$
• D. Least number which must be subtracted:$\left(i\right)8,\left(ii\right)41,\left(iii\right)12,\left(iv\right)56,\left(v\right)4$
  Square root of the perfect square:
  $\left(i\right)19,\left(ii\right)22,\left(iii\right)37,\left(iv\right)26,\left(v\right)61$

Answer 1

The correct option is B Least number which must be subtracted:$\left(i\right)2,\left(ii\right)53,\left(iii\right)1,\left(iv\right)41,\left(v\right)31$

Square root of the perfect square:
$\left(i\right)20,\left(ii\right)44,\left(iii\right)57,\left(iv\right)28,\left(v\right)63$
For $402$

Nearest perfect square is $400$

$\sqrt{400}$ $=$ $20$

$402$ $-$ $400$ $=$ $2$

For $1989$

Nearest perfect square is $1936$

$\sqrt{1936}$ $=$ $44$

$1936$ $-$ $1989$ $=$ $53$

For $3250$

Nearest perfect square is $3249$

$\sqrt{3249}$ $=$ $57$

$3250$ $-$ $3249$ $=$ $1$

For $825$

Nearest perfect square is $784$

$\sqrt{784}$ $=$ $28$

$825$ $-$ $784$ $=$ $41$

For $4000$

Nearest perfect square is $3969$

$\sqrt{3969}$ $=$ $63$

$4000$ $-$ $3969$ $=$ $31$

From this, Option B is correct answer.