Evaluate: $$\sqrt{248 + \sqrt{52 + \sqrt{144}}}$$
$$= \sqrt{248 + \sqrt{52 + 12}}$$ $$(\sqrt{144} = 12)$$
$$= \sqrt{248 + \sqrt{64}}$$
$$= \sqrt{248 + 8}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\sqrt{64} = 8)$$
$$= \sqrt{256}$$
$$= 16$$ $$ (\sqrt{256} = \sqrt{ 16 \times 16} = 16)$$
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. $$(i)\ 402$$ $$(ii)\ 1989$$ $$(iii)\ 3250$$ $$(iv)\ 825$$ $$(v)\ 4000$$
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.
If 3
Simplify : $$\sqrt {45} - 3\sqrt {20} + 4\sqrt {5}$$.
If $$\sqrt { 3 } = 1.732 ,$$ then find the value of : $$\sqrt { 27 } + \sqrt { 75 } + \sqrt { 108 } - \sqrt { 243 }$$
Arrange in Ascending order $$3\sqrt{2} , \sqrt{3}, 4\sqrt{4}$$
Find the least number which must be subtracted from each of the following numbers to make them a perfect square. Also find the square root of the perfect square number so obtained: $$984$$
Find the least number which must be subtracted from each of the following numbers to make them a perfect square. Also find the square root of the perfect square number so obtained: $$8934$$
Find the least number which must be subtracted from each of the following numbers to make them a perfect square. Also find the square root of the perfect square number so obtained: $$11021$$
Find the least number which must be added to each of the following numbers to make them a perfect square. Also, find the square root of the perfect square number so obtained: $$1750$$