Question

ajuda
1 --trabalhando com radicais efetue as multiplicações
a) √120÷√15
b)6√108/2√36
c) 3√4×3√5
d √4× √25× √1

Raciocine os denominadores abaixo

a) 3/√3

b) 5/ √7
c) 2/ √2-6

Answer 1

a)
  √120÷√15=√8=√2³=2√2

b)
  $\frac{6 \sqrt{108} }{2 \sqrt{36} } = \frac{6 \sqrt{2^2.3^3} }{2.6} = \frac{6.2.3 \sqrt{3} }{2.6} =3 \sqrt{3}$

c)
  3√4×3√5=3×2×3√5=18√5

d)
  √4×√25×√1=2×5×1=10

racionalizar

a)
   $\frac{3}{ \sqrt{3} } = \frac{3. \sqrt{3} }{ \sqrt{3}. \sqrt{3} } = \frac{3 \sqrt{3} }{ \sqrt{3^2} } = \frac{3 \sqrt{3} }{3} = \sqrt{3}$

b)
   $\frac{5}{ \sqrt{7} } = \frac{5. \sqrt{7} }{ \sqrt{7}. \sqrt{7} } = \frac{5 \sqrt{7} }{ \sqrt{7^2} } = \frac{5 \sqrt{7} }{7}$

c)

$\frac{2}{ \sqrt{2}-6 } = \frac{2( \sqrt{2}+6) }{( \sqrt{2}-6)( \sqrt{2}+6) } =$

$\frac{2( \sqrt{2}+6) }{2-36} = \frac{2( \sqrt{2}+6) }{-34} =- \frac{( \sqrt{2} +6)}{17} = \frac{- \sqrt{2}-6 }{17}$

Answer 2

1) 

a) $\sqrt{120}\div\sqrt{15}=2\sqrt{2}\sqrt{15}\div\sqrt{15}=2\sqrt{2}$

b) $\dfrac{6\sqrt{108}}{2\sqrt{36}}=\dfrac{6\sqrt{3}\sqrt{36}}{2\sqrt{36}}=3\sqrt{3}$

c) $3\sqrt{4}\times3\sqrt{5}=(3\times3)\sqrt{4\times5}=9\sqrt{20}=9\cdot2\sqrt{5}=18\sqrt{5}$

d) $\sqrt{4}\times\sqrt{25}\times\sqrt{1}=\sqrt{4\times25\times1}=\sqrt{100}=10$

2)

a) $\dfrac{3}{\sqrt{3}}=\dfrac{3\sqrt{3}}{3}=\sqrt{3}$

b) $\dfrac{5}{\sqrt{7}}=\dfrac{5\sqrt{7}}{7}$

c) $\dfrac{2}{\sqrt{2}-6}=\dfrac{2(\sqrt{2}+6)}{(\sqrt{2}-6)(\sqrt{2}+6)}=\dfrac{2\sqrt{2}+12}{2-36}=\dfrac{2\sqrt{2}+12}{-34}=\dfrac{\sqrt{2}+6}{-17}$