Question

$\sqrt[3]{8}$
$\sqrt[4]{625} \\\sqrt[4]{10000} \\\sqrt[3]{27} \\\sqrt[5]{32} \\\sqrt{1296} \\\sqrt{10000} \\\sqrt{2500}$

Answer 1

Você deve procurar um número que multiplicado por si mesmo pode dar o radical

$\bold{\sqrt[4]{\bold{625}}=} \\\\ 625 = 5*5*5*5 \qquad 625=5^4 \\\\ \bold{\sqrt[4]{\bold{625}}=\sqrt[4]{\bold{5^4}}=5}}$

----------------------------------------------

$\bold{\sqrt[4]{\bold{10000}}=} \\\\ 10000= 10*10*10*10 \qquad 10000=10^4 \\\\ \bold{\sqrt[4]{\bold{10000}}=\sqrt[4]{\bold{10^4}}=10}}$

----------------------------------------------

$\bold{\sqrt[3]{\bold{27}}=} \\\\ 27= 3*3*3 \qquad 27=3^3 \\\\ \bold{\sqrt[3]{\bold{27}}=\sqrt[3]{\bold{3^3}}=3}}$

------------------------------------------------

$\bold{\sqrt[5]{\bold{32}}=} \\\\ 32 = 2*2*2*2*2 \qquad 32=2^5 \\\\ \bold{\sqrt[5]{\bold{32}}=\sqrt[5]{\bold{2^5}}=2}}$

------------------------------------------------

$\bold{\sqrt[]{\bold{1296}}=} \\\\ 1296=2*2*2*2*3*3*3*3\qquad 1296=2^4*3^4 \\\\ \bold{\sqrt[]{\bold{1296}}=\sqrt[]{\bold{2^4*3^4}}=2^2*3^2= 4*9=36}}$

--------------------------------------------------

$\bold{\sqrt[]{\bold{10000}}=} \\\\ 10000= 10*10*10*10 \qquad 10000=10^4 \\\\ \bold{\sqrt[]{\bold{10000}}=\sqrt[]{\bold{10^4}}=10^2=100}}$

------------------------------------------------------

$\bold{\sqrt[3]{\bold{8}}=} \\\\ 8=2*2*2 \qquad 8=2^3 \\\\ \bold{\sqrt[3]{\bold{8}}=\sqrt[3]{\bold{2^3}}=2}}$

------------------------------------------------------

$\bold{\sqrt[]{\bold{2500}}=} \\\\ 2500= 2*2*5*5*5*5 \qquad 2500=2^2*5^4 \\\\ \bold{\sqrt[]{\bold{2500}}=\sqrt[]{\bold{2^2*5^4}}=2*5^2= 2*25=50}}$

:)