If n is a positive integer, then \left(\left(\right. \textrm{ } \sqrt{3} + 1 \textrm{ } \left.\right)\right)^{2 n} - \left(\left(\right. \textrm{ } \sqrt{3} - 1 \textrm{ } \left.\right)\right)^{2 n} is :

Engineering

Mathematics

Application of Binomial Theorem and Summation Of Series

Question

If n is a positive integer, then ${(\sqrt{3} + 1)}^{2 n} - {(\sqrt{3} - 1)}^{2 n}$ is :

an odd positive integer

a rational number other than positive integers

an even positive integer

an irrational number

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If $n = 1, {(\sqrt{3} + 1)}^{2} - {(\sqrt{3} - 1)}^{2} = 4 \sqrt{3}$

An irrational number.