Question

What is the greatest integer less than or equal to

(2+\sqrt{3} )^2

Collected in the board: Square Root

Steven Zheng posted 1 day ago

Answer

(2+\sqrt{3} )^2

=7+4\sqrt{3}

Let

a =7+4\sqrt{3}

b =7-4\sqrt{3}

Then

a+b = 14

a = 14-b

b =7-4\sqrt{3} =(2-\sqrt{3} )^2<(2-\sqrt{1} )^2 =1

Therefore

the greatest integer less than or equal to a is 13

Steven Zheng posted 1 day ago

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