Question : The simplified value of $(\sqrt{3}+1)( 10+\sqrt{12})(\sqrt{12}-2)(5-\sqrt{3})$ is:
Option 1: 16
Option 2: 88
Option 3: 176
Option 4: 132
Correct Answer: 176
Solution :
Given: $(\sqrt{3}+1)( 10+\sqrt{12})(\sqrt{12}-2)(5-\sqrt{3})$
⇒ $(\sqrt{3}+1)( 10+2\sqrt{3})(2\sqrt{3}-2)(5-\sqrt{3})$
⇒ $(\sqrt{3}+1)×2(5+\sqrt{3})×2(\sqrt{3}-1)×(5-\sqrt{3})$
⇒ $4(\sqrt{3}+1)(\sqrt{3}-1)(5+\sqrt{3})(5-\sqrt{3})$
We know that, $a^2-b^2=(a+b)(a-b)$
Thus,
= $4(3-1)(25-3)$
= $4×2×22$
= $176$
Hence, the correct answer is 176.
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