Simplify : $$\sqrt {45} - 3\sqrt {20} + 4\sqrt {5}$$.
$$\sqrt {45}-3\sqrt {20}+4\sqrt {5}$$
$$=\sqrt {3\times 3\times 5}-3\sqrt {2\times 2\times 5}+4\sqrt {5}$$
$$=3\sqrt {5}--6\sqrt {5}+4\sqrt {5}$$
$$=7\sqrt {5}-6\sqrt {5}$$
$$=\sqrt {5}$$
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.
Evaluate: $$\sqrt{248 + \sqrt{52 + \sqrt{144}}}$$
If 3
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: $$1750$$