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fabi965
@fabi965
October 2020
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Determine o quociente de:
a)√300 b)√54 c)√7+√2 : 10
√2 √2 6 √7-√2
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emicosonia
Determine o quociente de:
a)√
300
b)√
54
c)
√
7+
√
2
:
10
√2 √2 6 √7-√2
PASSO A PASSO
a)
√300
-------
√2
√300 √300.√2 √300.2 √600 10√6
--------- = ---------------- = ----------= ------------- = ------- =
5√6
(simplificou)
√2 √2.√2 √2.2 √4 2
fatorar √600 | 2 e √4| 2
300| 2 2| 2
150| 2 1/ =
√4 = √2.2.= √2² = 2
75| 3
25| 5
5| 5
1/
√600 = √2.2.2.3.5.5. = √2²2.3. 5² = √2²5².2.3 = 2.5 √2.3 =
10√6
b) √54 √54.√2 √54.2 √108 6√3
------- = ------------= ------------ = --------- = -------- =
3√3
√2 √2.√2 √2.2 √4 2
fatorar √108| 2 e √4 | 2
54| 2 2 | 2
27 | 3 1/
9 | 3
√4 = √2.2 = √2² = 2
3 | 3
1/
√108 = √2.2.3.3.3= √2²3².3= 2.3√3 = 6√3
c) √7 + √2 10
------------- : --------- é o memos QUE
6 √7 - √2
√7 + √2
-----------
6
_______________ duvisão conserva o 1º e INVERTE multiplicando o 2º
10
-----------
√7 - √2
√7 + √2 √7 - √2 (√7+√2)(√7-√2) √7√7 - √7√2 + √2√7 - √2√2
------------- x ------------- = ----------------------- = -----------------------------------------------
6 10 6(10) 60
√7.7 - √7.2 + √2.7 - √2.2
= --------------------------------------------
60
√49 - √14 + √14 - √4
= ------------------------------------
60
7 + 0 - 2 5 1
= ------------------- = ------ = ------ = 1/12
60 60 12
fatorando √49 |7 e √4|2
7 | 7 2| 2
1/ 1/
√49 = √7.7 = √7² = 7 √4 = √2.2 = √2² = 2
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a)√300 b)√54 c)√7+√2 : 10
√2 √2 6 √7-√2
PASSO A PASSO
a) √300
-------
√2
√300 √300.√2 √300.2 √600 10√6
--------- = ---------------- = ----------= ------------- = ------- = 5√6 (simplificou)
√2 √2.√2 √2.2 √4 2
fatorar √600 | 2 e √4| 2
300| 2 2| 2
150| 2 1/ = √4 = √2.2.= √2² = 2
75| 3
25| 5
5| 5
1/
√600 = √2.2.2.3.5.5. = √2²2.3. 5² = √2²5².2.3 = 2.5 √2.3 = 10√6
b) √54 √54.√2 √54.2 √108 6√3
------- = ------------= ------------ = --------- = -------- = 3√3
√2 √2.√2 √2.2 √4 2
fatorar √108| 2 e √4 | 2
54| 2 2 | 2
27 | 3 1/
9 | 3 √4 = √2.2 = √2² = 2
3 | 3
1/
√108 = √2.2.3.3.3= √2²3².3= 2.3√3 = 6√3
c) √7 + √2 10
------------- : --------- é o memos QUE
6 √7 - √2
√7 + √2
-----------
6
_______________ duvisão conserva o 1º e INVERTE multiplicando o 2º
10
-----------
√7 - √2
√7 + √2 √7 - √2 (√7+√2)(√7-√2) √7√7 - √7√2 + √2√7 - √2√2
------------- x ------------- = ----------------------- = -----------------------------------------------
6 10 6(10) 60
√7.7 - √7.2 + √2.7 - √2.2
= --------------------------------------------
60
√49 - √14 + √14 - √4
= ------------------------------------
60
7 + 0 - 2 5 1
= ------------------- = ------ = ------ = 1/12
60 60 12
fatorando √49 |7 e √4|2
7 | 7 2| 2
1/ 1/
√49 = √7.7 = √7² = 7 √4 = √2.2 = √2² = 2