Question

Simplificando o radical, fatore cada uma das expressões, colocando em evidência o fator comum:

a) 3 - √18

b) 10 + √8

c) 10 + √200

d) 2 + √12

e) 3 + √27

f) 10 - √50

g) 7 - √98

Answer 1

Olá João.


Fatorando e simplificando as expressões.


$\mathsf{A-}\\\\\mathsf{3 - \sqrt{18}}\\\mathsf{3-\sqrt{2\cdot3^2}}\\\mathsf{3-3\sqrt{2}}\\\mathsf{3\cdot(1-\sqrt{2})}\\\\\\\mathsf{B-}\\\\\mathsf{10+\sqrt{8}}\\\mathsf{10+\sqrt{2^2\cdot2}}\\\mathsf{10+2\sqrt{2}}\\\mathsf{2\cdot(5+\sqrt{2})}\\\\\mathsf{C-}\\\\\mathsf{ 10 + \sqrt{200}}\\\mathsf{10+\sqrt{10^2\cdot2}}\\\mathsf{10+10\sqrt{2}}\\\mathsf{10\cdot(1+\sqrt{2})}\\\\\\\mathsf{D-}\\\\\mathsf{2+\sqrt{12}}\\\mathsf{2+\sqrt{2^2\cdot3}}\\\mathsf{2+2\sqrt{3}}\\\mathsf{2\cdot(1+\sqrt{3})}$

$\mathsf{E-}\\\\\mathsf{3+\sqrt{27}}\\\mathsf{3+\sqrt{3^2\cdot3}}\\\mathsf{3+3\sqrt{3}}\\\mathsf{3\cdot(1+\sqrt{3})}\\\\\mathsf{F-}\\\\\mathsf{10-\sqrt{50}}\\\mathsf{10-\sqrt{5^2\cdot2}}\\\mathsf{10-5\sqrt{2}}\\\mathsf{5\cdot(2-\sqrt{2})}\\\\\\\mathsf{G-}\\\\\mathsf{7-\sqrt{98}}\\\mathsf{7-\sqrt{7^2\cdot2}}\\\mathsf{7-7\sqrt{2}}\\\mathsf{7\cdot(1-\sqrt{2})}$


Dúvidas? comente.