Question

01)Calcule.
a) √50-√72+√2-√8=
b) √300-√108+√3-√27=
c)^3√54+^3√250-^3√16=
d)^4√162-^4√32-^4√2=
e) √8+^3√16-√18+^3√54=

02) Calcule.
a)^3√7×^3√2=
b) √5×√8×√3=
c) 5^4√2×7^4√5=
d) 70^5√20:10^5√2=
e) 60^3√30:5^3√15=
f) √2×^3√5=
g)^3√3×^4√2=
h) √5×^3√4=
i)^10√3×^5√8=
j)^12√3×^6√5=
​

Answer 1

01) Calcule (soma e subtração de radicais):

$a) \sqrt{50} - \sqrt{72}+ \sqrt{2} - \sqrt{8}=$

  $5\sqrt{2}-6\sqrt{2}+\sqrt{2}-2\sqrt{2}=$

  $(5-6+1-2)\sqrt{2}=$

 $-2\sqrt{2}$

$b) \sqrt{300}- \sqrt{108}+ \sqrt{3}- \sqrt{27} =$

   $10\sqrt{3}- 6\sqrt{3}+ \sqrt{3}-3\sqrt{3}=$

  $(10-6+1-3)\sqrt{3}=$

  $2\sqrt{3}$

$c) \sqrt[3]{54}+\sqrt[3]{250}-\sqrt[3]{16}=$

   $3\sqrt[3]{2}+5\sqrt[3]{2}-2\sqrt[3]{2}=$

   $6\sqrt[3]{2}$

$d)$ $\sqrt[4]{162}-\sqrt[4]{32}-\sqrt[4]{2}=$

  $3\sqrt[4]{2}-2\sqrt[4]{2}-\sqrt[4]{2}=$

  $(3-2-1)\sqrt[4]{2}=$

  $0$  

$e) \sqrt{8}+ \sqrt[3]{16}- \sqrt{18}+\sqrt[3]{54}=$

  $\sqrt{8}-\sqrt{18}+\sqrt[3]{16}+\sqrt[3]{54}=$

  $2\sqrt{2}-3\sqrt{2}+2\sqrt[3]{2}+3\sqrt[3]{2}=$

  $-\sqrt{2}+ 5\sqrt[3]{2}=$

  $5\sqrt[3]{2}-\sqrt{2}=$

02) Calcule (multiplicação e divisão de radicais):

Só podemos multiplicar radicais se os índices foram iguais. Multiplicamos as bases e repetimos os índices.

a)  $\sqrt[3]{7} . \sqrt[3]{2} =$ $\sqrt[3]{2.7}=$ $\sqrt[3]{14}$

b) $\sqrt{5}.\sqrt{8}.\sqrt{3}=$ $\sqrt{5.8.3} =\sqrt{120} = 6\sqrt{5}$

c) $5. \sqrt[4]{2} . 7\sqrt[4]{5}=$ 5.7 $\sqrt[4]{2.5}=$ 35$\sqrt[4]{10}$

d) $70\sqrt[5]{20}:20\sqrt[5]{2} =$ $70:20$.$\sqrt[5]{20:2}=$$3,5\sqrt[5]{10}$

e)60$\sqrt[3]30}:5\sqrt[3]{15}=$$60:5\sqrt[3]{30:15}=12\sqrt[3]{2}$

Os próximos radicais não têm índices iguais. Vamos reduzir ao mesmo índice para resolver:

f) $\sqrt{2}.\sqrt[3]{5}=$ $\sqrt[6]{2^3}. \sqrt[6]{5^2}= \sqrt[6]{8.25} =\sqrt[6]{200}$

g)$\sqrt[3]{3}.\sqrt[4]{2}=$ $\sqrt[12]{3^4}.\sqrt[12]{2^3}= \sqrt[12]{81.8}=\sqrt[12]{648}$

h) $\sqrt{5} . \sqrt[3]{4} =$ $\sqrt[6]{5^3} . \sqrt[6]{4^2}=\sqrt[6]{125.16}=\sqrt[6]{2000}$

i)$\sqrt[10]{3} . \sqrt[5]{8} =$ $\sqrt[10]{3}.\sqrt[10]{8^{2} } = \sqrt[10]{3^}.8^{2} }= \sqrt[10]{3.64}=\sqrt[10]{192}$

j)$\sqrt[12]{3}.\sqrt[6]{5}=$$\sqrt[12]{3.5^2}=\sqrt[12]{3.25}=\sqrt[12]{75}$