Question

transforme em um unico radical:
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Answer 1

Explicação passo-a-passo:

a)

$\sf \sqrt{3}\cdot\sqrt{5}$

$\sf =\sqrt{3\cdot5}$

$\sf =\red{\sqrt{15}}$

b)

$\sf \sqrt[3]{7}\cdot\sqrt[3]{11}$

$\sf =\sqrt[3]{7\cdot11}$

$\sf =\red{\sqrt[3]{77}}$

c)

$\sf \sqrt{2}\cdot\sqrt{5}\cdot\sqrt{7}$

$\sf =\sqrt{2\cdot5\cdot7}$

$\sf =\red{\sqrt{70}}$

d)

$\sf \sqrt[12]{50}\cdot\sqrt[12]{10}$

$\sf =\sqrt[12]{50\cdot10}$

$\sf =\red{\sqrt[12]{500}}$

f)

$\sf =\dfrac{\sqrt{12}\cdot\sqrt{15}}{\sqrt{8}}$

$\sf =\dfrac{\sqrt{12\cdot15}}{\sqrt{8}}$

$\sf =\dfrac{\sqrt{180}}{\sqrt{8}}$

$\sf =\dfrac{6\sqrt{5}}{\sqrt{8}}$

$\sf =\dfrac{6\sqrt{5}}{\sqrt{8}}\cdot\dfrac{\sqrt{8}}{\sqrt{8}}$

$\sf =\dfrac{6\sqrt{40}}{8}$

$\sf =\dfrac{6\cdot2\sqrt{10}}{8}$

$\sf =\dfrac{12\sqrt{10}}{8}$

$\sf =\red{\dfrac{3\sqrt{10}}{2}}$

g)

$\sf \dfrac{\sqrt{\sqrt[3]{4}}\cdot\sqrt{\sqrt[3]{10}}}{\sqrt[6]{120}}$

$\sf =\dfrac{\sqrt[6]{4}\cdot\sqrt[6]{10}}{\sqrt[6]{120}}$

$\sf =\dfrac{\sqrt[6]{40}}{\sqrt[6]{120}}$

$\sf =\dfrac{\sqrt[6]{40}}{\sqrt[6]{120}}\cdot\dfrac{\sqrt[6]{120}}{\sqrt[6]{120}}$

$\sf =\dfrac{\sqrt[6]{4800}}{120}$

$\sf =\dfrac{2\sqrt[6]{75}}{120}$

$\sf =\red{\dfrac{\sqrt[6]{75}}{60}}$