Question

Efetue as operações:
A) √80 - √2=
B) √204 ÷ √17
C) √6 × √30
D) √18 - √128 + √32

Por favor me ajudem !!!

Answer 1

Olá.

Teremos de fatorar para chegar na forma irredutível.
A
$\sqrt{80}-\sqrt{2}=\\\\\sqrt{2^4\cdot5}-\sqrt{2}=\\\\4\sqrt{5}-\sqrt{2}\approx\\\\4\cdot2,24-1,41\approx\\\\8,96-1,41\approx\\\\\boxed{7,55}$

B
$\sqrt{204}/\sqrt{17}=\\\\2\sqrt{51}/\sqrt{17}\approx\\\\2\cdot7,14/4,12\approx\\\\14,28/4,12\approx\\\\14,28/4,12\approx\\\\\boxed{3,47}$

C
$\sqrt{6}\cdot\sqrt{30}=\\\\\sqrt{6\cdot30}=\\\\\sqrt{180}=\\\\\sqrt{2^2\cdot3^2\cdot5}=\\\\2\cdot3\sqrt{5}=\\\\6\sqrt{5}\approx\\\\6\cdot2,24\approx\\\\\boxed{13,44}$

D
$\sqrt{18}-\sqrt{128}+\sqrt{32}=\\\\ \sqrt{2\cdot3^2}-\sqrt{2^7}+\sqrt{2^5}=\\\\ 3\sqrt{2}-2^3\sqrt{2}+2^2\sqrt{2}=\\\\ 3\sqrt{2}-8\sqrt{2}+4\sqrt{2}=\\\\ (3-8+4)\sqrt{2}=\\\\ \boxed{-\sqrt{2}\approx-1,41}$

Qualquer dúvida, deixe nos comentários.
Bons estudos.

Answer 2

$a) \ \sqrt{80}-\sqrt{2}\\ \\ \ =\sqrt{16\cdot 5}-\sqrt{2} \\ \\ \ =\sqrt{16}\cdot \sqrt{5}-\sqrt{2} \\ \\ \ =4\sqrt{5}-\sqrt{2} \\ \\ \\ a) \ \sqrt{80}-\sqrt{20}\\ \\ \ =\sqrt{16\cdot 5}-\sqrt{4\cdot5} \\ \\ \ =\sqrt{16}\cdot \sqrt{5}-\sqrt{4}\cdot\sqrt{5} \\ \\ \ =4\sqrt{5}-2\sqrt{5} \\ \\ \ =2\sqrt{5}$
-------------------------------------------------------------------------------
$b)\ \sqrt{204}:\sqrt{17} =\sqrt{ \frac{204}{17}} = \sqrt{12}= \sqrt{4\cdot3}= \sqrt{4}\cdot\sqrt{3}=2\sqrt{3}$
-------------------------------------------------------------------------------
$c)\sqrt{6}\times\sqrt{30} \\ =\sqrt{6}\times\sqrt{6\times 5} \\ =\sqrt{6\times6\times 5} \\ =\sqrt{36 \times 5}\\ =\sqrt{36} \times\sqrt{5}\\ =6\sqrt{5}$
-------------------------------------------------------------------------------
$d)\ \sqrt{18}- \sqrt{128}+ \sqrt{32}\\ \\ \ = \sqrt{9\cdot2}- \sqrt{64\cdot2}+ \sqrt{16\cdot2}\\ \\ \ = \sqrt{9}\cdot\sqrt{2}- \sqrt{64}\cdot\sqrt{2}+ \sqrt{16}\cdot\sqrt{2}\\ \\ \ = 3\sqrt{2}-8\sqrt{2}+ 4\sqrt{2}\\ \\ \ =-\sqrt{2}$