Question

Calcule e simplifique
A) √2.√5    B) √3.√15  C)√2.√98  D)√20.√9/20  E)√200.√2      F)√50.√36    G)√0,4.√10        H)√8.√1/2

Answer 1

a) 

$\sqrt{2}\cdot\sqrt{5}\Rightarrow\sqrt{2\cdot5}\Rightarrow\boxed{\sqrt{10}}$

b)

$\sqrt{3}\cdot\sqrt{15}\Rightarrow\sqrt{3\cdot(3\cdot5)}\Rightarrow\sqrt{3^2\cdot5}\Rightarrow\boxed{3\sqrt{5}}$

c)

$\sqrt{2}\cdot\sqrt{98}\Rightarrow\sqrt{2\cdot(2\cdot7^2)}\Rightarrow\sqrt{2^2\cdot7^2}\Rightarrow2\cdot7\Rightarrow\boxed{14}$

d)

$\sqrt{20}\cdot\sqrt{\frac{9}{20}}\Rightarrow\sqrt{20\cdot\frac{9}{20}}\Rightarrow\sqrt{9}\Rightarrow\boxed{3}$

e)

$\sqrt{200}\cdot\sqrt{2}\Rightarrow\sqrt{400}\Rightarrow\sqrt{20^2}\Rightarrow\boxed{20}$

f)

$\sqrt{50}\cdot\sqrt{36}\Rightarrow\sqrt{(2\cdot5^2)\cdot(6^2)}\Rightarrow5\cdot6\sqrt{2}\Rightarrow\boxed{30\sqrt{2}}$

g)

$\sqrt{0,4}\cdot\sqrt{10}\Rightarrow\sqrt{\frac{4}{10}\cdot10}\Rightarrow\sqrt{4}\Rightarrow\boxed{2}$

h) Tente fazê-la empregando os cálculos acima!

Espero ter ajudado!

Answer 2

$a)~~ \sqrt{2} . \sqrt{5} = \sqrt{2.5} = \sqrt{10}$

$b)~~ \sqrt{3} . \sqrt{15} = \sqrt{3} . \sqrt{3.5} = \sqrt{3} . \sqrt{3} . \sqrt{5} = \sqrt{3.3} . \sqrt{5} =\\\\ \sqrt{9} . \sqrt{5} =3 \sqrt{5}$

$c)~~ \sqrt{2} . \sqrt{98} = \sqrt{2} . \sqrt{2.49} = \sqrt{2}. \sqrt{2}. \sqrt{49} = (\sqrt{2.2} ).7=7 \sqrt{4} =\\\\=7.2=14$

$d)~~ \sqrt{20} . \sqrt{ \frac{9}{20} } = \sqrt{20} . \frac{ \sqrt{9} }{ \sqrt{20} } =\\\\= \frac{ 3\sqrt{20 } }{ \sqrt{20} } =3$

$e)~~ \sqrt{200} . \sqrt{2} = \sqrt{2.100} . \sqrt{2} = \sqrt{2} . \sqrt{2} . \sqrt{100} =10 \sqrt{4} =2.10=20$

$f)~~ \sqrt{50} . \sqrt{36} = 6\sqrt{2.25}=6.5 \sqrt{2} =30 \sqrt{2}$

$g)~~ \sqrt{0,4} . \sqrt{10} = \sqrt{10~.~0,4} = \sqrt{4} =2$

$h)~~ \sqrt{8} . \sqrt{ \frac{1}{2} } = \sqrt{8} . \frac{ \sqrt{1} }{ \sqrt{2} } = \frac{ \sqrt{8} }{ \sqrt{2} } = \sqrt{ \frac{8}{2} } = \sqrt{4} =2$