Question

explain whether the following numbers are rational or irrational. justify your answer.
$( \sqrt{3 + \frac{1}{ \sqrt{3} } } ) {}^{2}$
​

Answer 1

Step-by-step explanation:

${( \sqrt{3} + \frac{1}{ \sqrt{3} } })^{2} \\ = ( \sqrt{3})^{2} + 2 \times \sqrt{3} \times \frac{1}{ \sqrt{3} } + ( \frac{1}{ \sqrt{3} } )^{2} \\ = 3 + 2 + \frac{1}{3} \\ = \frac{9 + 6 + 1}{3} \\ = \frac{16}{3}$

Hope it helps you