Question

If a=5+2√6 then find the value of √a²+1/a

Answer 1

$\sqrt{a {}^{2} } = a$

$= a + \frac{1}{a}$

$= \frac{ {a}^{2} + 1}{a}$

(5+2√6)^2+1 / 5+2√6

25+24+20√6+1 / 5+2√6

50+20√6 / 5+2√6

10(5+2√6) / 5+2√6

=10

Thus the required answer is 10...