Question

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Answer 1

Recuerda que:

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

1)

$= {( \sqrt{15} + \sqrt{50} ) }^{2} \\ = { \sqrt{15} }^{2} + 2( \sqrt{15} )( \sqrt{50} ) + { \sqrt{50} }^{2} \\ = 15 + 2 \sqrt{750} + 50 \\ = 65 + 2 \sqrt{ {5}^{2} \times 30} \\ = 65 + 10 \sqrt{30}$

2)

$= \frac{ \sqrt{8} - 3 \sqrt{4} }{ \sqrt{2} } \\ = \frac{2 \sqrt{2} - 6 }{ \sqrt{2} } \\ = \frac{4 - 6 \sqrt{2} }{2} \\ = 2 - 3 \sqrt{2}$

3)

$= ( 2(\sqrt[3]{5} + 3))(2( \sqrt[3]{5} - 3)) \\ = 4( \sqrt[3]{ {5}^{2} } - {3}^{2} ) \\ = 4 (\sqrt[3]{25} - 9) \\ = 4 \sqrt[3]{25} - 36$