Question

calcule as potencias


A)(√2²)=
B)(∛9)²=
C)(4√5)³=
D)(√2+√3)²=
E)(√15)²=

Answer 1

Resposta:

a) $(\sqrt{2})^3 = \sqrt{2^3} = \sqrt{2^2.2}=\sqrt{2^2}\sqrt{2}=2\sqrt{2} </p><p>\\\\\sqrt[n]{a}^m=\sqrt[n]{a^m}$(use para reescrever a raiz)

b) $(\sqrt[3]{9})^2=\sqrt[3]{9^2}=\sqrt[3]{81}=\sqrt[3]{3^3.3}=\sqrt[3]{3^3}\sqrt[3]{3}=3\sqrt[3]{3}$

c) $(4\sqrt{5})^3=4^3.\sqrt{5}^3=64.5\sqrt{5}=320\sqrt{5}$

d) $(\sqrt{2}+\sqrt{3})^2=\sqrt{2^2}+2\sqrt{2}\sqrt{3^2}=2+2\sqrt{6}+\sqrt{3^2}=2+2\sqrt{6}+3=5+2\sqrt{6} \\\\\</p><p>\\\(a+b)^2=a^2+2ab+b^2$ (use para desenvolver a expressão)

e) $(\sqrt{15})^2=15$