Question

calcule
a) ⁴√625=

b) ³√216=

c) ⁵√-1=

d) ³√1000=​

Answer 1

   $\boxed{\begin{array}{l}\tt a)\\\begin{array}{c|c}\sf625&\sf5\\\sf125&\sf5\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\implies \sf625=5^4\\\sf\sqrt[\sf4]{\sf625}=\sqrt[\sf\backslash\!\!\!4]{\sf5^{\backslash\!\!\!4}}=5\\\tt b)\\\begin{array}{c|c}\sf216&\sf2\\\sf108&\sf2\\\sf54&\sf2\\\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\implies \sf 216=2^3\cdot3^3\\\sf \sqrt[\sf3]{\sf216}=\sqrt[\sf\backslash\!\!\!3]{\sf 2^{\backslash\!\!\!3}\cdot 3^{\backslash\!\!\!3}}=2\cdot3=6\end{array}}$

$\boxed{\begin{array}{l}\tt c)\\\sf\sqrt[\sf3]{\sf-1}=-1\\\tt d)\\\sf \sqrt[\sf3]{\sf1000}=\sqrt[\sf\backslash\!\!\!3]{10^{\sf\backslash\!\!\!3}}=10\end{array}}$