Square and Square Roots
A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.
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. $$(i)\ 402$$ $$(ii)\ 1989$$ $$(iii)\ 3250$$ $$(iv)\ 825$$ $$(v)\ 4000$$
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.
$$\therefore \sqrt {3969} = 63$$
A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.
Evaluate: $$\sqrt{248 + \sqrt{52 + \sqrt{144}}}$$
If 3
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Arrange in Ascending order $$3\sqrt{2} , \sqrt{3}, 4\sqrt{4}$$
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