Question

Find the value of h in following expression :
$h = \sqrt{2 + \sqrt{3} } + \sqrt{2 - \sqrt{3} }$

Answer 1

Answer:

$h = \sqrt{6}$

Step-by-step explanation:

${h}^{2} = (2 + \sqrt{3} ) + 2 \sqrt{(2 + \sqrt{3})(2 - \sqrt{3}) } + (2 - \sqrt{3} ) \\ = > {h}^{2} = 4 + 2 \sqrt{( {2}^{2}) - {( \sqrt{3} )}^{2} } \\ = > {h}^{2} = 4 + 2 \sqrt{4 - 3} \\ = > {h}^{2} = 4 + 2 \sqrt{1} \\ = > {h}^{2} = 4 + 2 = 6 \\ = > {h }^{2} = 6 \\ = > h = \sqrt{6}$

Hope it helps...

Regards;

Leukonov/OLegion.