Question

simplify:(√3-✓5)² and (64/125)-⅔

Answer 1

$( { \sqrt{3} - \sqrt{5}) }^{2} = \: (a - b {)}^{2} \\ (a - b {)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ {( \sqrt{3} - \sqrt{5} )}^{2} = \: { (\sqrt{3} )}^{2} + ( { \sqrt{5} )}^{2} - 2 \times \sqrt{3} \times \sqrt{5}$
$= 3 + 5 - 2 \sqrt{15}$

$2) \: \: \: {(64 \div 125)}^{ - 2 \div 3}$
$= {( {4}^{3} \div {5}^{3}) }^{ - 2 \div 3}$
$(4 \div 5 {)}^{(3 \times - 2 \div 3)}$
$(4 \div 5 {)}^{ - 2} =( 5 \div 4 {)}^{2} \\ = 25 \div 16$
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