Question

Simplifique:
$\sqrt{576}$
$\sqrt[5]{243}$
$\sqrt[4]{4096}$
$\sqrt{14400}$
$\sqrt[6]{729}$
$\sqrt{2025}$
$\sqrt{ \frac{121}{144} }$

Answer 1

Fatorando, separadamente, os números: 576, 243, 4096, 14400, 729, 2025, 121, 144 (em anexo).

$\sqrt{576} =\sqrt{2^6 \cdot 3^2}= \sqrt{(2^2 \cdot 2^2 \cdot 2^2) \cdot 3^2}=(2 \cdot 2 \cdot 2) \cdot 3 =24\\ \\ \sqrt[5]{243} =\sqrt[5]{3^5}=3\\ \\ \sqrt[4]{4096}= \sqrt[4]{2^{12}} = \sqrt[4]{2^4 \cdot 2^4 \cdot 2^4}= 2 \cdot 2 \cdot 2 = 8\\ \\ \sqrt{14400}= \sqrt{2^6 \cdot 3^2 \cdot 5^2} = \sqrt{(2^2 \cdot 2^2 \cdot 2^2) \cdot 3^2 \cdot 5^2}= (2 \cdot 2 \cdot 2) \cdot 3 \cdot 5 = 120\\ \\ \sqrt[6]{729}= \sqrt[6]{3^6}=3$

$\sqrt{2025}= \sqrt{3^4 \cdot 5^2} = \sqrt{(3^2 \cdot 3^2) \cdot 5^2}= (3 \cdot 3) \cdot 5 = 45\\ \\ \sqrt{\dfrac{121}{144}} =\sqrt{\dfrac{11^2}{2^4 \cdot 3^2}} = \sqrt{\dfrac{11^2}{(2^2 \cdot 2^2) \cdot 3^2}} =\dfrac{11}{(2 \cdot 2) \cdot 3}= \dfrac{11}{12}$

Bons estudos!