The smallest number to be added to 680621 to | vedclass

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Question

(A) To find the smallest number to be added to $680621$ to make it a perfect square,we first find the square root of $680621$ using the long division

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) To find the smallest number to be added to $680621$ to make it a perfect square,we first find the square root of $680621$ using the long division method.Step $1$: Group the digits in pairs from right to left: $68, 06, 21$.Step $2$: Find the largest square less than or equal to $68$,which is $8^2 = 64$. So,the first digit is $8$.Step $3$: Subtract $64$ from $68$ to get $4$,and bring down the next pair $06$ to get $406$.Step $4$: Double the quotient $8$ to get $16$. Find a digit $x$ such that $16x 	imes x \leq 406$. For $x = 2$,$162 	imes 2 = 324$. For $x = 3$,$163 	imes 3 = 489$ (too large).Step $5$: Subtract $324$ from $406$ to get $82$,and bring down the next pair $21$ to get $8221$.Step $6$: The current quotient is $82$. Double it to get $164$. Find a digit $y$ such that $164y 	imes y \leq 8221$. For $y = 4$,$1644 	imes 4 = 6576$. For $y = 5$,$1645 	imes 5 = 8225$.Since $8225 > 8221$,the next perfect square is $825^2 = 680625$.Step $7$: The number to be added is $680625 - 680621 = 4$.

The smallest number to be added to $680621$ to make the sum a perfect square is

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