Question

propiedades de los radicales, por favor

Answer 1

Saludos
1)
$\sqrt[np]{ a^{p} } = a^{ \frac{p}{np} } = a^{ \frac{1}{n} } = \sqrt[n]{a}$
ejo
$\sqrt[4]{9} = \sqrt[4]{ 3^{2} } = 3^{ \frac{2}{4} } = 3^{ \frac{1}{2} } = \sqrt{3}$

2)
$\sqrt[n]{ab} = (ab)^{ \frac{1}{n}} = a^{ \frac{1}{n} } b^{ \frac{1}{n} } = \sqrt[n]{a} \sqrt[n]{b}$
$\sqrt[]{3 x^{2} y} = (3 x^{2} y)^{ \frac{1}{2}} = 3^{ \frac{1}{2} } x^{2} ^{ \frac{1}{2} }y^{ \frac{1}{2} } = \sqrt[]{3} \sqrt[]{ x^{2}} \sqrt[]{y}$
3)
$\sqrt[n]{ \frac{a}{b} } = \frac{\sqrt[n]{a} }{\sqrt[n]{b} }$
$\sqrt[]{ \frac{3}{ x^{3} } } = \frac{\sqrt{3} }{\sqrt{ x^{3}} }$
4)
$(\sqrt[n]{a}) ^{p} = (a{ \frac{1}{n} } )^{p}= a^{( \frac{1}{n} )p} = (a^{p} )^{ \frac{1}{n} } = \sqrt[n]{ a^{p} }$
$( \sqrt{-5} )^{4} =\sqrt({-5} )^{4}=25$
5)
$\sqrt[m]{ \sqrt[n]{a} } = (a^{ \frac{1}{n} } )^{ \frac{1}{m} } = a^{ (\frac{1}{n})( \frac{1}{m} ) } = a^{ \frac{1}{mn} } = \sqrt[nm]{a}$
$\sqrt[3]{ \sqrt{3} } = \sqrt[6]{3}$


Espero te sirva