Question

Ao resolver a fração:
$\frac{\sqrt{30} }{\sqrt{3} \sqrt{5}}$
temos o resultado de:

a)2
b)$\sqrt{2}$
c)10
d)$\sqrt{5}$
e)$\sqrt{3}$

Answer 1

Olá,

$\dfrac{\sqrt{30}}{\sqrt{3}\sqrt{5}}=\dfrac{\sqrt{30}}{\sqrt{3\cdot5}}=\dfrac{\sqrt{30}}{\sqrt{15}}\\\\\dfrac{\sqrt{30}}{\sqrt{15}}\cdot\dfrac{\sqrt{15}}{\sqrt{15}}=\\\\\dfrac{\sqrt{30\cdot15}}{15}=\dfrac{\sqrt{2\cdot3\cdot5\cdot3\cdot5}}{15}=\\\\\dfrac{\sqrt{2\cdot3^2\cdot5^2}}{15}=\dfrac{3\cdot5\sqrt{2}}{15}\\\\\dfrac{15\sqrt{2}}{15}=\sqrt{2}$

Alternativa (b) √2