Question

simplyfythe following
(√5+√3)²​

Answer 1

${\mathscr{\underline{\underline{\blue{Question}}}}}$

$( \sqrt{5} + \sqrt{3} ) ^{2}$

${\mathscr{\underline{\underline{\blue{Solution}}}}}$

Using the identity -

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

$( \sqrt{5} + \sqrt{3} {)}^{2}$

${ \sqrt{5} }^{2} + { \sqrt{3} }^{2} + 2 \sqrt{5} \sqrt{3}$

$5 + 3 + 2 \sqrt{15}$

$8 + 2 \sqrt{15}$

${\large{\mathsf{\purple{More\:Identities\:-}}}}$

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

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

• ${a}^{2}– {b}^{2}= (a + b)(a – b)$

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

• $(a + b + c)^{2}= {a}^{2}+ {b}^{2} + {c}^{2}+ 2ab + 2bc + 2ca$

• $(a + b)^{3} = {a}^{3} + {b}^{3}+ 3ab (a + b)$

• $(a – b)^{3}= {a}^{3} – {b}^{3}– 3ab (a – b)$

• ${a}^{3 }+ {b}^{3}+ {c}^{3} – 3abc = (a + b + c)({a}^{2} + {b}^{2 }+ {c}^{2}– ab – bc – ca)$