Respuesta :

DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ [/tex]

Using identity :

  • [tex] {(a + b)}^{2} = {a}^{2} + b {}^{2} + 2ab[/tex]

  • [tex]( \sqrt{5 }{+ \sqrt{2{}^{} } } ) {}^{2} [/tex]

  • [tex]( \sqrt{5} ) {}^{2} + ( \sqrt{2} ) {}^{2} + 2( \sqrt{5} )( \sqrt{2} )[/tex]

  • [tex]5 + 2 + 2 \sqrt{10} [/tex]

  • [tex]7 + 2 \sqrt{10} [/tex]

therefore, the correct choice is :

  • [tex] \mathrm{C.) \: \: 7 + 2 \sqrt{10} }[/tex]

Solution:

[tex]( \sqrt{5} + \sqrt{2} {)}^{2} \\ [/tex]

[tex]by \: \: \: using \: \: \: the \: \: \: formula \: \: (a + b) ^{2} = {a}^{2} + 2ab \: + {b}^{2} \: \: we \: \: \: get \\ ( \sqrt{5} {)}^{2} + 2( \sqrt{5}) \: (\sqrt{{2)}} + ( \sqrt{2) }^{2} \\ = \sqrt{5} \times \sqrt{5} + 2 \sqrt{5 \times 2} + \sqrt{2} \times \sqrt{2} \\ = 5 + 2 \sqrt{10} + 2 \\ = 7 + 2 \sqrt{10} [/tex][/tex]

Answer:

(C) 7+2√10

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