Question

$if \: a \: equal \: to \: 7 - 4 \sqrt{3} \: \: find \: the \: value \: of \: \sqrt{a + } \frac{1}{ \sqrt{a} ?}$
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Answer 1

$a = 7 - 4 \sqrt{3} \\ \frac{1}{a} = \frac{1}{7 - 4 \sqrt{3} } \\ after \: rationalising \: the \: denominator \\ \: \frac{1}{a} = 7 + 4 \sqrt{3} \\ a + \frac{1}{a} = 7 - 4 \sqrt{3} + 7 + 4 \sqrt{3}$

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