Question

me ajudem não estou conseguindo resolver essa expressão: ⎷43+⎷31+⎷21+√13+√7+√3+√1

Answer 1

$\sqrt{ 43 +\sqrt{31 + \sqrt{21 + \sqrt{ 13 + \sqrt{ 7+ \sqrt {3+{\sqrt{ 1 } } }} }}}} \\\\ \sqrt{ 43 +\sqrt{31 + \sqrt{21 + \sqrt{ 13 + \sqrt{ 7+ \sqrt {3+ 1 } } }} }}} \\\\ \sqrt{ 43 +\sqrt{31 + \sqrt{21 + \sqrt{ 13 + \sqrt{ 7+ \sqrt {4 } }} }}} \\\\ \sqrt{ 43 +\sqrt{31 + \sqrt{21 + \sqrt{ 13 + \sqrt{ 7 + 2 }} }}} \\\\ \sqrt{ 43 +\sqrt{31 + \sqrt{21 + \sqrt{ 13 + \sqrt{ 9 }} }}} \\\\ \sqrt{ 43 +\sqrt{31 + \sqrt{21 + \sqrt{ 13 + 3} }}}$


$\sqrt{ 43 +\sqrt{31 + \sqrt{21 + \sqrt{16} }}} \\\\\\ \sqrt{ 43 +\sqrt{31 + \sqrt{21 + \sqrt{16} }}} \\\\\\ \sqrt{ 43 +\sqrt{31 + \sqrt{21 + 4 }}} \\\\\\ \sqrt{ 43 +\sqrt{31 + \sqrt{25 }}} \\\\\\ \sqrt{ 43 +\sqrt{31 + 5}} \\\\\\ \sqrt{ 43 +\sqrt{36}} \\\\\\ \sqrt{ 43 + 6} \\\\\\ \sqrt{ 49 } = \boxed{7}$