Question

1) Simplifique os radicais

a) √324

b) ⁴√64

c) √2500

d) √0,25

e) √36
-----
49

f)³√8
----
27

g) ³√3⁵+3⁵+3⁶
​

Answer 1

Resposta:

a) 18

b) $2\sqrt{2}$

c) 50

d) 0,5

e) $\frac{6}7}$

f) $\frac{2}{3}$

g) $3\sqrt[3]{45}$

Explicação passo a passo:

a) $\sqrt{324}=\sqrt{2^2*9^2}=2*9=18$

b) $\sqrt[4]{64}=\sqrt[4]{2^4*4}=2*\sqrt[4]{4}=2\sqrt{2}$

c) $\sqrt{2500}=\sqrt{2^2*5^2*5^2} =2*5*5=50$

d) $\sqrt{0,25}=\sqrt{0,5^2}=0,5$

e) $\sqrt{\frac{36}{49}}=\frac{\sqrt{36}}{\sqrt{49}}=\frac{\sqrt{2^2*3^2}}{\sqrt{7^2}}=\frac{2*3}{7}=\frac{6}7}$

f) $\sqrt[3]{\frac{8}{27}}=\frac{\sqrt[3]{8}}{\sqrt[3]{27}}=\frac{\sqrt[3]{2^3}}{\sqrt[3]{3^3}}=\frac{2}{3}$

g)

$\sqrt[3]{3^5+3^5+3^6}= \\\\ \sqrt[3]{243+243+729}= \\\\ \sqrt[3]{1215}= \sqrt[3]{3^3*45}=3\sqrt[3]{45}$