Question

How much added to non perfect square to make it perfect square?

Answer 1

Answer:

Step-by-step explanation:

Depends upon number

Answer 2

$\underline{\underline{\Huge{\textbf{Question:}}}}$

What is the least number that must be added to a Non-perfect square to make it a Perfect square ?

$\underline{\huge{\textbf{Steps:}}}$

$\diamondsuit{}$ Use$\textsf{\: Division method of finding square root}$ to find $\textit{nearest\: perfect\: square\: higher\: than\: the\: Non-perfect\: square}$.
($\textbf{For\: Steps, refer\: below}$)

$\diamondsuit{}$ The difference between the Nearest higher perfect square and the Non-perfect square is the required least number that must be added to Non-perfect square to make it a perfect square.

$\underline{\textbf{Required least Number = Nearest Higher perfect square - Non-perfect square}}$



$\underline{\LARGE{\textbf{Example:}}}$

What is the least number that must be added to a 6412 to make it a Perfect square ?

$\underline{Solution:}$ Using Division Method of finding square root,

$\begin{array}{a|b|c}8 & \: \: \overline{64}\: \overline{12}&80 \\ &64\: \: \\ \cline{1-2} 160&\quad\quad 12\\ &\quad\quad 0 \\\cline{1-2}&\quad\quad 12\end{array}$

$\textit{Final Quotient= 80}$

$\textit{Square root of Nearest Lower Perfect square = 80}$

$\implies \sf \textsf{Nearest lower perfect square = (80)^{2} = 1600}$

$\implies \sf \textit{Nearest Higher perfect square = (80+1)^{2}= (81)^{2} = 6561}$

$\mathbf{(80)^{2} < (6412) < (81)^{2}}$
$\mathbf{(6400) < (6412) < (6561)}$

$\implies \large{\textsf{Required least No. = 6561 - 6412 =\underline{\large{\textbf{149}}}}}$



$\underline{\Large{\textsf{Division Method of Finding Square root:}}}$

$\underline{\large{\textit{Step-1:}}}$
Consider the Number and Place $bars$ on each digit starting from left to right.

$\underline{\large{\textit{Step-2:}}}$
Consider the $\sf \textsf{first pair as dividend}$ and find the largest number which when squared is equal or less than the first pair

$\underline{\large{\textit{Step-3:}}}$
Perform the division and note the $\sf \textsf{quotient}$ and the $\sf \textsf{remainder}$

$\underline{\large{\textit{Step-4:}}}$
Place the second pair of digits to the right of the remainder, to form a $\sf \textsf{new dividend}$

$\underline{\large{\textit{Step-5:}}}$
The new divisor has twice the quotient as its digits to the left and another digit is chosen such that the number formed by merging twice the quotient and this digit multiplied by the same digit is less than or equal to the new dividend.

$\underline{\large{\textit{Step-6:}}}$
$\sf \textsf{Division is continued till the remainder is zero}$

The number formed by placing the new quotient to the right of the previous quotient is the Final quotient

Final Quotient is the $\underline{\textbf{square\: root\: of\: the\: number}}$ considered in the first place.

Here,
While placing bars, there may be a $\textsf{single digit}$ as $\textit{first pair}$, if the number of digits in the number are odd.

$\underline{\large{\textsf{Another Case:}}}$
The $\textsf{Remainder \neq 0}$, when the number considered in the first place is a $\sf \textsf{Non-perfect square}$

Final quotient is square root of Nearest Perfect square lower than the Non perfect square.

$\implies \textsf{Squaring the Final Quotient gives the Nearest Lower Perfect square}$

Adding 1 to to the final quotient gives the square root of Nearest Perfect square higher than the Non perfect square.