Subjective Type

Find the least number which must be subtracted from each of the following so as to get a perfect square. Also find the square root of the perfect square so obtained. $$(i)\ 402$$ $$(ii)\ 1989$$ $$(iii)\ 3250$$ $$(iv)\ 825$$ $$(v)\ 4000$$

Solution

In order to find the least number to be subtracted from the given no.,
we must find a smaller perfect square number, closest to the given number.

i) $$402$$
The closest smaller perfect square number is $$400$$
Difference $$=402-400 = 2$$
Hence, $$2$$ must be subtracted from $$402$$ in order to make it a perfect square.
$$\therefore \sqrt {400} = 20$$

ii) $$1989$$
The closest smaller perfect square number is $$1936$$.
Difference $$=1989-1936 = 53$$
Hence, $$53$$ must be subtracted from $$1989$$ in order to make it a perfect square.
$$\therefore \sqrt {1936} = 44$$

iii) $$3250$$
The closest smaller perfect square number is $$3249$$.
Difference $$=3250-3249 = 1$$
Hence, $$1$$ must be subtracted from $$3250$$ in order to make it a perfect square.
$$\therefore \sqrt {3249} = 57$$

iv) $$825$$
The closest smaller perfect square number is $$784$$.
Difference $$=825-784 = 41$$
Hence, $$41$$ must be subtracted from $$825$$ in order to make it a perfect square.
$$\therefore \sqrt {784} = 28$$

v) $$4000$$
The closest smaller perfect square number is $$3969$$.
Difference $$=4000-3969 = 31$$
Hence, $$31$$ must be subtracted from $$4000$$ in order to make it a perfect square.
$$\therefore \sqrt {3969} = 63$$


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