Respostas
Resposta:
Explicação passo-a-passo:
Racionalize:
´´é ELIMINAR A raiz DO DENOMINADOR
a)
a)
5 5√2 5√2 5√2 5√2
------ = --------- = --------------- = ------------ = -----------
√2 √2(√2) √2x2 √4 2 (dica √4 = 2)
b)
b)
8
--------
∛2² atençãooooooooooooo
8 8∛2¹
----- = -------------- vejaaaaaaaaaaaaaaaaaaa
∛2² ∛2².∛2¹
8∛2¹
----------
∛2¹⁺² vejaaaaaaaaaaaa
8∛2
-------
∛2³ ( elimina a ∛(raiz cubica) com o (³))
8∛2
--------- = 4∛2
2
c)
5
--------------- vejaaaaaaaaaaaaaaaa
3 + √2
5(3 - √2)
--------------------------------
(3 + √2)(3 - √2) vejaaaa
5(3 - √2)
----------------------------------
9 - 3√2 + 3√2 - √2√2
5(3 - √2)
---------------------
9 + 0 - √2x2
5(3 - √2)
--------------------
9 - √4 ======> (√4 = 2)
5 (3- √2)
-----------------
9 - 2
5( 3 - √2)
---------------
7
d)
9 9√3 9√3 9√3 9√3
------ = ------------ = ------------- = -----------= ---------- 3√3
√3 √3√3 √3x3 √9 3 (dica √9 = 3)
e)
14
-----
⁸√7⁵ vejaaaaaaaaaaaaaaa
14.⁸√7³
-------------
⁸√7⁵. ⁸√7³ vejaaaaaaaaaaaaaa
14.⁸√343
------------
⁸√7⁵⁺³
14.⁸√343
--------------
⁸√7⁸ elimina a ⁸√(raiz oitava) com o (⁸)
14.⁸√343
--------------- = 2.⁸√343
7
f)
4
-----
7 - √5
4(7 + √5)
---------------
(7 - √5)( 7 + √5) vejaaaaaaaaaaaaaaa
4(7 + √5)
---------------------------------
49 + 7√5 - 7√5 - √5√5
4(7 + √5)
------------------
49 + 0 - √5x5
4(7 + √5)
-----------------
49 - √25 ===>(dica √√25 = 5)
4(7 + √5)
----------------
49 - 5
4(7 + √5) ( 7 + √5)
---------------- = -------------------
44 11
g)
g)
10
-------
√3 - 2
10(√3 + 2)
----------------------
(√3 -2)(√3 + 2)
10(√3 + 2)
------------------------------
√3√3 + 2√3 - 2√3 - 4
10(√3 + 2)
------------------
√3x3 + 0 - 2
10(√3 + 2)
----------------
√9 - 2 (√9= 3)
10(√3 + 2)
----------------
3 - 2
10(√3 + 2)
----------------- = 10(√3 + 2) ou 10(2 + √3)
1