Question

simplifique os radicais sabendo que as variáveis representam números reais não negativos ​

Answer 1

C)  ³√6²

D)  ²√4^4 * b³

E) 14 * y^4

F) 2 * √3y

G) ³√9

H) 100

I) (2/3) - (2 * √7)

J) √2 + 1

K) √3 + 2

L)  (1 - √2)/2

1) Para responder o problema proposto, vamos resolver cada equação dada encontrando o maximo divisor comum (MDC). Logo, teremos:

C) ^12√6^8 = $\sqrt[3]{6^{2} }$

MDC (12, 8) = 4

12, 8 | 2

6, 4 | 2

3, 2 | 2

3, 1 | 3

1, 1

D) 4^√a^8 * 6^6 = $\sqrt[2]{a^{4} * b^{3} }$

MDC (4, 8, 6) = 2

4, 8, 6 | 2

2, 4, 3 | 2

1, 2, 3 | 2

1, 1, 3 | 3

1, 1, 1

E) 2 *  3^√7^3 * y^12 = 14 * y^4

MDC (3, 3, 12) = 3

3, 3, 12 | 3

1, 1, 4 | 2

1, 1, 2 | 2

1, 1, 1

F) 4^ √144 * y^2 = 4^√2^4 * 3^2 * y^2 = 2 * 4^√3^2 * y^2 = 2 * √3y

MDC(4, 2) = 2

4, 2 | 2

2, 1 | 2

1, 1

G) 9^√3^6 = $\sqrt[3]{9}$

MDC(9, 6) = 3

9, 6 | 2

9, 3 | 3

3, 1 | 3

1, 1

H) 3^√10^6 = 10^2 = 100

MDC (3, 6) = 3

3, 6 | 2

3, 3 | 3

1, 1

I) (4 - 12*√7) / 6 = (2/3) - (2 * √7)

J) (√18 + 3) / 3 = (√3^2 * 2 + 3) / 3 = (3 * √2/3) + (3/3) = √2 + 1

18/ 2

9/ 3

3/ 3

1

K) (√75 + 10) / 5 = (√5^2 * 3 + 10) /5 = (5 * √3/ 5) + (10/5) = √3 + 2

75 / 5

15/ 5

3/ 3

1

L) 7 - √98 / 14 = (7 - √2 * 7^2) / 14 = (7/14) - ((7 * √2) / 14) = (1 - √2)/2

98 / 2

49 / 7

7 / 7

1