Question

ayuden plisss esos 4 cuatros problemas

Answer 1

Aplicamos:

$\sqrt{a+b-2 \sqrt{a.b} } = \sqrt{a} - \sqrt{b}$


$\sqrt{12-2 \sqrt{35} }$

$\sqrt{7+5-2 \sqrt{7.5} } = \sqrt{7} - \sqrt{5}$



$\sqrt{11-2 \sqrt{18} }$

$\sqrt{9+2+2 \sqrt{9.2} } = \sqrt{9} - \sqrt{2}$


$\sqrt{4+\sqrt{12} }$

$\sqrt{4+2\sqrt{3} }$

$\sqrt{3+1+2\sqrt{3.1} }$

$\sqrt{3} + \sqrt{1}$

$\sqrt3} +1$


$\sqrt{a} - \sqrt{b} = \sqrt{ \frac{a+c}{2} } - \sqrt{ \frac{a-c}{2} }$

siendo:  $c= \sqrt{ a^{2} -b}$

$c= \sqrt{ a^{2} -b}$

$c= \sqrt{ 4^{2} -15}$

$c= \sqrt{ 16 -15}$

$c= \sqrt{1}$

c = 1

$c= \sqrt{ 4 - \sqrt{15} } = \sqrt{\frac{4+1}{2} } - \sqrt{ \frac{4-1}{2} } = \sqrt{ \frac{5}{2} }- \sqrt{ \frac{3}{2} } = \frac{ \sqrt{10} }{2} - \frac{ \sqrt{6} }{2}$