Question

What least must to be subtracted from the following to make them a perfect square? 361298

Answer 1

Step-by-step explanation:

square root of 361298 by long division method-

6 | 36 12 98 ( 601

| 36

-----------------

1201 | 00 12 98

| 12 01

----------------

97

-----------------

Remainder = 97

Therefore if we subtract 97 from 361298, it will be a perfect square of 601.

361298 - 97 = 361201 ( 361201 = 601^2)

Therefore 97 is the least number which must be subtracted from 361298 to make it a perfect square.

Answer 2

$\large\underline{\sf{Solution-}}$

Given number is 361298.

Since, we have to find the least number that must be subtracted from the 361298 to make it a perfect square.

So, we use long division to find the remainder that should be subtracted from the given number.

Thus,

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:601 \:\:}}}\\ {\underline{\sf{6}}}& {\sf{\:\:361298 \:\:}} \\{\sf{}}& \underline{\sf{\:\:36 \: \: \:   \:  \:  \:  \ }} \\ {\underline{\sf{1201}}}& {\sf{\:\: \: \: \: \: 001298 \:  \:  \: \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: 1201\:  \:}} \\ {\underline{\sf{}}}& {\sf{\: \:  \: \: \: \: \: \: 97\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

So, it means 97 must be subtracted from 361298 to make it a perfect square.

Thus, Required number is 361298 - 97 = 361201.

So,

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:601 \:\:}}}\\ {\underline{\sf{6}}}& {\sf{\:\:361201 \:\:}} \\{\sf{}}& \underline{\sf{\:\:36 \: \: \:   \:  \:  \:  \ }} \\ {\underline{\sf{1201}}}& {\sf{\:\: \: \: \: \: 001201 \:  \:  \: \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: 1201\:  \:}} \\ {\underline{\sf{}}}& {\sf{\: \:  \: \: \: \: \: \: 00\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

Hence,

$\rm \implies\:\boxed{ \tt{ \: \sqrt{361201} = 601 \: }}$