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Question 15 Marks
Find the least number which must be subtracted from $825$ so as to get a perfect square. Also find the square root of the perfect square so obtained.
Answer


This shows that $28$ is less than $825$ by $41$.
This means, if we subtract the remainder from the number, we get a perfect square,
So, the required least number is $41$.
Therefore, the required perfect square is $825 – 41 = 784$
Hence, $\sqrt {784} $$=28$.
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Question 25 Marks
Find the least number which must be subtracted from $3250$ so as to get a perfect square. Also find the square root of the perfect square so obtained.
Answer


This shows that $57^2$ is less than $3250$ by $1$.
This means, if we subtract the remainder from the number, we get a perfect square,
So, the required least number is $1$.
Therefore, the required perfect square is $3250 – 1 = 3249$
Hence, $\sqrt {3249}$$=57$.
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Question 35 Marks
Find the least number which must be subtracted from $1989$ so as to get a perfect square. Also find the square root of the perfect square so obtained.
Answer


This shows that $44^2$ is less than $1989$ by $53$.
This means, if we subtract the remainder from the number,
we get a perfect square, So, the required least number is $53$.
Therefore, the required perfect square is $1989 – 53 = 1936$.
Hence, $\sqrt {1936} $$=44$.
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Question 45 Marks
Find the least number which must be subtracted from $402$ so as to get a perfect square. Also find the square root of the perfect square so obtained.
Answer


This shows that $20^2$ is less than $402$ by $2$. This means, if we subtract the remainder from the number, we get a perfect square, So, the required least number is $2$.
Therefore, the required perfect square is $402 – 2 = 400$.
Hence, $\sqrt {400} $$=20$.
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