Question

Question: (3+root 3)(2+ root 3)^2= ?

Answer 1

Answer:

$( {(3 + \sqrt{3})(2 + \sqrt{3}) })^{2} \\ {(3(2 + \sqrt{3}) + \sqrt{3}(2 + \sqrt{3}))}^{2} \\ {(6 + 3 \sqrt{3} + 2 \sqrt{3} + 3) }^{2} \\ \ {(6 + 5 \sqrt{3} + 3) }^{2} \\ {(9 + 5 \sqrt{3} )}^{2} \\ \bold \red { {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab } \\ = {9}^{2} + {(5 \sqrt{3}) }^{2} + 2 \times 9 \times 5 \sqrt{3} \\ = 81 + 25 \times 3 + 90 \sqrt{3} \\ = 81 + 75 + 90 \sqrt{3} \\ = 156 + 90 \sqrt{3}$

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