Simplificar Radicales (2851)

radicales
simplificar_radicales

Opera y simplifica:

a) $\sqrt{625}$
b) $\sqrt{a^2 : 0.01}$
c) $\sqrt{\sqrt{16}}$
d) $\sqrt{\sqrt[3]{729}}$

SOLUCIÓN

a) $\sqrt{625} = \sqrt{5^4}=\sqrt{5^2 \cdot 5^2}=5 \cdot 5 = 25$

b) $\sqrt{a^2 : 0.01}=\sqrt{\frac{a^2}{0.01}}=\sqrt{\frac{a^2}{10^{-2}}}= \sqrt{a^2 \cdot 10^2} =a \cdot 10 = 10a$

c) $\sqrt{\sqrt{16}}= \sqrt[4]{16}= \sqrt[4]{2^4} = 2$

d) $\sqrt{\sqrt[3]{729}}$
$\left. \begin{array}{c|c}729 & 3\cr243 & 3 \cr81 & 3 \cr27 & 3 \cr9 & 3 \cr3 & 3 \cr1\end{array} \right.$
$\sqrt{\sqrt[3]{729}} = \sqrt[6]{729}= \sqrt[6]{3^6}=3$

SOLUCIÓN

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