Question

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1. Aplica las propiedades de la radicación y calcula
a =√81×100=
b =³√216×125=
c =³√17×(-343)×5120=
d =√144×36×25=
e=³√4³x5³x2⁶=
f =⁶√(a²)⁵.(a³)⁸.a²=

2. Coloca el símbolo > o <, en cada caso.
a. -12_____8
b. 7 ____ -8
c. 14 ______ 27
d. 39 _____-45
e. -19 _______ -20
3 .Hallar la raíz cuadrada de
√53824
√68715

Answer 1

1.

a)$\sqrt{(81)(100)}=\sqrt{(9^{2})(10^{2})} =(9^{2})^{\frac{1}{2}}(10^{2})^{\frac{1}{2}}=(9)(10)=90$

b)$\sqrt[3]{(216)(125)}=\sqrt[3]{(6^{3})(5^{3})} =(6^{3})^{\frac{1}{3}}(5^{3})^{\frac{1}{3}}=(6)(5)=30$

c)$\sqrt[3]{(17)(-343)(5120)}=\sqrt[3]{(17)(-7^{3})(5120)} =(-7^{3})^{\frac{1}{3}}\sqrt[3]{(17)(5120)}=(-7)\sqrt[3]{87040}$

d)$\sqrt{(144)(36)(25)}=\sqrt{(12^{2})(6^{2})(5^{2})} =(12^{2})^{\frac{1}{2}}(6^{2})^{\frac{1}{2}}(5^{2})^{\frac{1}{2}}=(12)(6)(5)=360$

e) $\sqrt[3]{(4^{3})(5^{3})(2^{6})} =(4^{3})^{\frac{1}{3}}(5^{3})^{\frac{1}{3}}(2^{6})^{\frac{1}{3}}=(4)(5)(2^{2})=(4)(5)(4)=80$

f) $\sqrt[6]{(a^{2})^{5}(a^{3})^{8}(a^{2})} =\sqrt[6]{(a^{10})(a^{24})(a^{2})}=\sqrt[6]{(a^{10+24+2})}=\sqrt[6]{(a^{36})}=(a^{36})^{\frac{1}{6}}=a^{6}$

2

a)<

b)>

c)<

d)>

e)>

3

a)$\sqrt{53824}=\sqrt{(64)(841)}=\sqrt{(8^{2})(29^{2})}={(8^{2})^{\frac{1}{2}}(29^{2})^{\frac{1}{2}}}=(8)(29)=232$

b)$\sqrt{68715}=\sqrt{(9)(7635)}=\sqrt{(3^{2})(7635)}={(3^{2})^{\frac{1}{2}}\sqrt{(7635)}=3\sqrt{7635}=262.1354.....$