Question

Transforma a un radical
simple.

Answer 1

Respuesta:

              $3+\sqrt{2}$

Explicación paso a paso:

$\sqrt{11+\sqrt{72} }$

Descomponemos la raíz cuadrada de 72.

$\sqrt{36 *2} = \sqrt{36} * \sqrt{2} = 6\sqrt{2}$

$\sqrt{11+ 6\sqrt{2} }$

$Tambien: 2 + 9 = 11$

$\sqrt{2+6\sqrt{2}+9 }$

$Aplicando: ( x+y)=x^{2} +2(x)(y)+y^{2}$

$2(\sqrt{2} )(\sqrt{9} ) = 2 (\sqrt{2} )(3) =6\sqrt{2}, entonces : (\sqrt{2}+3 )^{2} = (\sqrt{2} )^{2} +2(\sqrt{2} )(3)+(3)^{2}$  

$(\sqrt{2} +3)^{2} = 2+6\sqrt{2} +9$    

$\sqrt{11+\sqrt{72} } = \sqrt{(\sqrt{2}+3)^{2} }$

$Luego: \sqrt{11+\sqrt{72} } = 3+\sqrt{2} }$