Question

1 - Decomponha os radicandos em fatores primos e extraia as seguintes raizes

A) V 225



B) V 324



C) V 784



D) V 1764

Answer 1

A) √225 = 15

B) √324 = 18

C) √784 = 28

D) √1764 = 42

Explanation:

English Translation

Decompose radicands into prime factors and extract the following roots.

Note that the V represents the square root symbol.

A) V 225

B) V 324

C) V 784

D) V 1764

Solution

A) √225

Doing the division in the long method manner

225 | 3

75 | 3

25 | 5

5 | 5

1

225 = 3 × 3 × 5 × 5 = 3² × 5²

√225 = √(3² × 5²) = 3 × 5 = 15

B) √324

324 | 2

162 | 2

81 | 3

27 | 3

9 | 3

3 | 3

1

324 = 2 × 2 × 3 × 3 × 3 × 3 = 2² × 3⁴ = 2²× 9²

√324 = √(2² × 9²) = 2 × 9 = 18

C) √784

784 | 2

392 | 2

196 | 2

98 | 2

49 | 7

7 | 7

1

784 = 2 × 2 × 2 × 2 × 7 × 7 = 2⁴ × 7² = 4²× 9²

√784 = √(4² × 7²) = 4 × 7 = 28

D) √1764

1764 | 2

882 | 2

441 | 3

147 | 3

49 | 7

7 | 7

1

1764 = 2 × 2 × 3 × 3 × 7 × 7 = 2² × 3² × 7²

√1764 = √(2² × 3² × 7²) = 2 × 3 × 7 = 42

Hope this Helps!!!