Question

MULTIPLICACIÓN Y DIVISIÓN DE RADICALES
a. 9 √2 ⋅ 3 √8 =
b. 5 √3 ⋅ 2 √75 =
c. 15 √32 : 3 √2 =
d. 48 √6 : 3 √ 3 2 =
e. 6 √32 ⋅ 5 √8 12 =

Answer 1

Respuesta:

es como 49 482 4647 392924

Answer 2

Respuesta:

$\boxed{\mathbf{\begin{matrix}a).=108&b).=150&c).=20\\\\d).=4\sqrt{3}&\frac{2\sqrt{2}}{5\sqrt{203}}\end{matrix}}}$

Explicación paso a paso:

$a).\\9\sqrt{2}*3\sqrt{8}=9\sqrt{2}*3\sqrt{(2)(4)}=\\\\=9\sqrt{2}*3\sqrt{2}\sqrt{4}=9\sqrt{2}*3*2\sqrt{2}=\\\\=9*3*2\sqrt{2}\sqrt{2}=54(\sqrt{2})^{2}=\\\\=54*2=108$

$b).\\5\sqrt{3}*2\sqrt{75}=5\sqrt{3}*2\sqrt{(3)(25)}=\\\\=5\sqrt{3}*2\sqrt{3}\sqrt{25}=5\sqrt{3}*2*5\sqrt{3}=\\\\=5*2*5*(\sqrt{3})^{2}=50*(3)=150$

$c).\\15\sqrt{32}:3\sqrt{2}=15\sqrt{32}/3\sqrt{2}=\frac{15\sqrt{(2)(16)}}{3\sqrt{2}}=\\\\=\frac{15\sqrt{2}\sqrt{16}}{3\sqrt{2}}=\frac{15*4*\sqrt{2}}{3\sqrt{2}}=\\\\=\frac{60\sqrt{2}}{3\sqrt{2}}=\frac{60}{3}=20$

$d).\\48\sqrt{6}:3\sqrt{32}=\frac{48\sqrt{6}}{3\sqrt{32}}=\frac{48\sqrt{6}}{3*\sqrt{(2)(16)}}=\\\\=\frac{48\sqrt{6}}{3*\sqrt{2}\sqrt{16}}=\frac{48\sqrt{6}}{3*4*\sqrt{2}}=\\\\=\frac{48\sqrt{6}}{12\sqrt{2}}=\frac{4\sqrt{6}}{\sqrt{3}}=4\sqrt{\frac{6}{3}}=\\\\=4\sqrt{3}$

$e).\\6\sqrt{32}:5\sqrt{812}=\frac{6\sqrt{32}}{5\sqrt{812}}=\frac{6\sqrt{(2)(16)}}{5\sqrt{(4)(203)}}=\\\\=\frac{6*4*\sqrt{2}}{5*2\sqrt{203}}=\frac{24\sqrt{2}}{10\sqrt{203}}=\\\\=\frac{2}{5}\sqrt{\frac{2}{203}}$