Answer:
The simplified version of [tex]\sqrt[3]{135}[/tex] is [tex]3\sqrt[3]{5}[/tex].
Step-by-step explanation:
The given expression is
[tex]\sqrt[3]{135}[/tex]
According to the property of radical expression.
[tex]\sqrt[n]{x}=(x)^{\frac{1}{n}}[/tex]
Using this property we get
[tex]\sqrt[3]{135}=(135)^{\frac{1}{3}}[/tex]
[tex]\sqrt[3]{135}=(27\times 5)^{\frac{1}{3}}[/tex]
[tex]\sqrt[3]{135}=(3^3\times 5)^{\frac{1}{3}}[/tex]
[tex]\sqrt[3]{135}=(3^3)^{\frac{1}{3}}\times (5)^{\frac{1}{3}}[/tex] [tex][\because (ab)^x=a^xb^x][/tex]
[tex]\sqrt[3]{135}=3\times \sqrt[3]{5}[/tex] [tex][\because \sqrt[n]{x}=(x)^{\frac{1}{n}}][/tex]
[tex]\sqrt[3]{135}=3\sqrt[3]{5}[/tex]
Therefore the simplified version of [tex]\sqrt[3]{135}[/tex] is [tex]3\sqrt[3]{5}[/tex].
