Question

1. Find the value of 5V6 + 3V6
3. Is the number (5 + V4)(5 – V4) rational or Irrational ?
4.Ifa = 6 + 2V3, find the value of
а-1/a​

Answer 1

Step-by-step explanation:

$1) \: 5 \sqrt{6} + 3 \sqrt{6} \\ \: \: \: = (5 + 3) \sqrt{6} \\ \: \: \: = 8 \sqrt{6} \\ \\ 2) \: (5 + \sqrt{4} )(5 - \sqrt{4} ) \\ by \: using \: identiy \: (x + y)(x - y) = {x}^{2} - {y}^{2} \\ then \: x = 5 \: and \: y \: = \sqrt{4} \\ so \: put \: the \: value \: of \: x \: and \: y \\ (5 + \sqrt{4} )(5 - \sqrt{4} ) \\ = {5}^{2} - { \sqrt{4} }^{2} \\ = 25 - 4 \\ = 21 \\ It \: is \: written \: in \: the\: form \: of \: \frac{p}{q}(q≠0).\\So, \: it \: is \: a \: rational \: number \:$

$=6 + 2 \sqrt{3} - \frac{1}{6 + 2 \sqrt{3}} \\ = \frac{(6 + 2 \sqrt{3})(6 + 2 \sqrt{3}) - 1}{6 + 2 \sqrt{3}} \\ = \frac{36 + 24 \sqrt{3} + 12 - 1}{6 + 2 \sqrt{3}} \\ = \frac{47 + 24 \sqrt{3}}{6 + 2 \sqrt{3}}$