radicales simplificar

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Calcula y simplifica:

– a) $\sqrt{3 \cdot 5^3} : \sqrt{27}$
– b) $\sqrt{\sqrt{\sqrt{256}}}$

SOLUCIÓN

– a)

$\sqrt{3 \cdot 5^3} : \sqrt{27}$

$\frac{\sqrt{3 \cdot 5^3}}{\sqrt{27}}$

$\frac{\sqrt{3 \cdot 5^2 \cdot 5}}{\sqrt{3^2 \cdot 3}}$

$\frac{5 \cdot \sqrt{3 \cdot 5}}{3 \cdot \sqrt{3}}$

$\frac{5 \cdot \cancel{\sqrt{3}} \cdot \sqrt{5}}{3 \cdot \cancel{\sqrt{3}}}$

$\frac{5 \cdot \sqrt{5}}{3}$

– b)

$\sqrt{\sqrt{\sqrt{256}}} = \sqrt{\sqrt{\sqrt{2^8}}} = \sqrt[8]{2^8} = 2$