Question

Simplifique os radicais. √∛2187

Answer 1

Resposta:

$\sqrt{ \sqrt[3]{2187} } = \sqrt[2 \times 3]{2187} = \sqrt[6]{2187} = 3 \sqrt[6]{3}$

Answer 2

Resposta:

$\boxed{\mathtt{3\sqrt[6]{3}}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{\sqrt{\sqrt[3]{2187}} =} \\\\ \mathsf{\left ( \sqrt[3]{2187} \right )^{\frac{1}{2}} =} \\\\ \mathsf{\left ( 2187^{\frac{1}{3}} \right )^{\frac{1}{2}} =} \\\\ \mathsf{2187^{\frac{1}{6}} =} \\\\ \mathsf{\left ( 3^7 \right )^{\frac{1}{6}} =} \\\\ \mathsf{3^{\frac{7}{6}} =} \\\\ \mathsf{\sqrt[6]{3^7} =} \\\\ \boxed{\boxed{\mathsf{3\sqrt[6]{3}}}}$