Question:-

Find the least number that must be added to 6203 to make it a perfect square. Also find the square root of this number.

Solution

Given number is 6203.

Now, we have to find the least number which must be added to 6203 to obtain a perfect square.

So, in order to find the least number which must be added to 6203 to obtain a perfect square, we use method of Long Division.

So, using long division method, we have

[tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{ \: \: \: \: 79 \: \: \: \: }}}\\ {\underline{\sf{7}}}& {\sf{6203}} \\{\sf{}}& \underline{\sf{49 \: \: \: \: }} \\ {\underline{\sf{149}}}& {\sf{1303}} \\{\sf{}}& \underline{\sf{1341}} \\ {\underline{\sf{}}}& {\sf{ \: \: \: 38}} \end{array}\end{gathered}\end{gathered} \\ \\ \end{gathered}[/tex]

So, from this we concluded that 38 must be added to 6203 to obtain a perfect square.

So, Required number = 6203 + 38 = 6241

Now, Consider

[tex]\begin{gathered}\sf \: \sqrt{6241} \\ \\ \end{gathered}[/tex]

So, using Long Division Method, we have

[tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{ \: \: \: \: 79 \: \: \: \: }}}\\ {\underline{\sf{7}}}& {\sf{6241}} \\{\sf{}}& \underline{\sf{49 \: \: \: \: }} \\ {\underline{\sf{149}}}& {\sf{1341}} \\{\sf{}}& \underline{\sf{1341}} \\ {\underline{\sf{}}}& {\sf{ \: \: 0 \: \: }} \end{array}\end{gathered}\end{gathered} \\ \\ \end{gathered}[/tex]

Hence,

[tex]\begin{gathered}\bf\implies \: \sqrt{6241} = 79 \\ \\ \end{gathered}[/tex]

[tex]\rule{190pt}{2pt}[/tex]

Answer:

[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:38 \qquad \: \\ \\& \qquad \:\sf \: 79 \end{aligned}} \qquad \: \\ \\ \end{gathered}[/tex]