Question

Simplifique os radicais e efetue as operações​

Answer 1

Explicação passo-a-passo:

a) $\sqrt{2}+\sqrt{32}$

   $32=2^{5}=2^{2}.2^{2}.2$

     $\sqrt{2}+\sqrt{32}=\sqrt{2}+\sqrt{2^{5}}=\sqrt{2}+\sqrt{2^{2}.2^{2}.2}=\sqrt{2}+2.2\sqrt{2}=\sqrt{2}+4\sqrt{2}=5\sqrt{2}$

-----------------------------------------------------------------------------------------------

b) $\sqrt{27}+\sqrt{3}$

   $27=3^{3}=3^{2}.3$

   $\sqrt{27}+\sqrt{3}=\sqrt{3^{3}}+\sqrt{3}=\sqrt{3^{2}.3}+\sqrt{3}=3\sqrt{3}+\sqrt{3}=4\sqrt{3}$

---------------------------------------------------------------------------------------------

c) $3\sqrt{5}+\sqrt{20}$

   $20=2^{2}.5$

   $3\sqrt{5}+\sqrt{20}=3\sqrt{5}+\sqrt{2^{2}.5}=3\sqrt{5}+2\sqrt{5}=5\sqrt{5}$

------------------------------------------------------------------------------------------

d) $2\sqrt{2}+\sqrt{8}$

   $8=2^{3}=2^{2}.2$

   $2\sqrt{2}+\sqrt{8}=2\sqrt{2}+\sqrt{2^{3}}=2\sqrt{2}+\sqrt{2^{2}.2}=2\sqrt{2}+2\sqrt{2}=4\sqrt{2}$

----------------------------------------------------------------------------------------

e) $\sqrt{27}+5\sqrt{3}$

   $27=3^{3}=3^{2}.3$

   $\sqrt{27}+5\sqrt{3}=\sqrt{3^{3}}+5\sqrt{3}=\sqrt{3^{2}.3}+5\sqrt{3}=3\sqrt{3}+5\sqrt{3}=8\sqrt{3}$

---------------------------------------------------------------------------------------

f) $2\sqrt{7}+\sqrt{28}$

   $28=2^{2}.7$

   $2\sqrt{7}+\sqrt{28}=2\sqrt{7}+\sqrt{2^{2}.7}=2\sqrt{7}+2\sqrt{7}=4\sqrt{7}$

--------------------------------------------------------------------------------------

g) $\sqrt{50}-\sqrt{98}$

   $50=2.5^{2}$   ;   $98=2.7^{2}$

   $\sqrt{50}-\sqrt{98}=\sqrt{2.5^{2}}-\sqrt{2.7^{2}}=5\sqrt{2}-7\sqrt{2}=-2\sqrt{2}$

-------------------------------------------------------------------------------------

h) $\sqrt{12}-6\sqrt{3}$

   $12=2^{2}.3$

   $\sqrt{12}-6\sqrt{3}=\sqrt{2^{2}.3}-6\sqrt{3}=2\sqrt{3}-6\sqrt{3}=-4\sqrt{3}$

------------------------------------------------------------------------------------

i) $\sqrt{20}-\sqrt{45}$

   $20=2^{2}.5$   ;   $45=3^{2}.5$

   $\sqrt{20}-\sqrt{45}=\sqrt{2^{2}.5}-\sqrt{3^{2}.5}=2\sqrt{5}-3\sqrt{5}=-\sqrt{5}$