Question

para efetuar (√3 + √2)(√27 - √2)

Answer 1

$( \sqrt{3} + \sqrt{2} )( \sqrt{27} - \sqrt{2} )= \sqrt{3} . \sqrt{27} - \sqrt{3} . \sqrt{2} + \sqrt{2} . \sqrt{27} - \sqrt{2} . \sqrt{2}$


$( \sqrt{3} + \sqrt{2} )( \sqrt{27} - \sqrt{2} )= \sqrt{81} - \sqrt{6} + \sqrt{54} - \sqrt{4}$


$( \sqrt{3} + \sqrt{2} )( \sqrt{27} - \sqrt{2} )= 9 - \sqrt{6} + \sqrt{54} - 2$

$( \sqrt{3} + \sqrt{2} )( \sqrt{27} - \sqrt{2} )= 7 - \sqrt{6} + \sqrt{54}$

$54 = 2.3.3.3 = 2. 3^2.3$

$( \sqrt{3} + \sqrt{2} )( \sqrt{27} - \sqrt{2} )= 7 - \sqrt{6} + \sqrt{2.3^2.3}$

$( \sqrt{3} + \sqrt{2} )( \sqrt{27} - \sqrt{2} )= 7 - \sqrt{6} + 3 \sqrt{6}$


$( \sqrt{3} + \sqrt{2} )( \sqrt{27} - \sqrt{2} )= 7 + 2 \sqrt{6}$


resp: $7+2 \sqrt{6}$

Answer 2

(√3 + √2)(√27 - √2)

√81 - √6 + √54 - √4     ⇒   fatorando 54 = √2.3².3

9 - √6  + √2.3².3  -  2

9 - √6 + 3√2.3  - 2

9 - √6 + 3√6 - 2

- 2 + 9 - √6 + 3√6

+ 7 + 2√6