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3 years ago

The value of (√5 + √2)2 (A) 7+ 2√5 (B) 1+ 5√2 (C) 7+2√10 (D) 7-2√10

Mathematics

2 answers:

sveta [45]3 years ago

8 0

$▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪$

Using identity :

${(a + b)}^{2} = {a}^{2} + b {}^{2} + 2ab$

$( \sqrt{5 }{+ \sqrt{2{}^{} } } ) {}^{2}$

$( \sqrt{5} ) {}^{2} + ( \sqrt{2} ) {}^{2} + 2( \sqrt{5} )( \sqrt{2} )$

$5 + 2 + 2 \sqrt{10}$

$7 + 2 \sqrt{10}$

therefore, the correct choice is :

$\mathrm{C.) \: \: 7 + 2 \sqrt{10} }$

hammer [34]3 years ago

3 0

<h3>Solution:</h3>

$( \sqrt{5} + \sqrt{2} {)}^{2} \\$

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

<h3>Answer:</h3>

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