Question

Oblicz:

a) (√10)²

b) √4¹⁰ (ta 10 odnosi się do 4. jeśli do całego pierwiastka to daję nawias)

c) ∛125²

d) ⁵√32³

e) (⁸√625)²

f) √√81 (czyli √81 jest piewiastkowany)

g) (∛√27)²

h) ∛√4³

i)(√∛49)³

j) ∛⁴√16⁶

Answer 1

√10²=10

√4¹⁰=√(4⁵)²=4⁵=1024

∛125²=∛(5³)²=∛(5²)³=5²=25

⁵√32³=⁵√(2³)⁵=8

⁸√625²=⁸√(5⁴)²=⁸√5⁸=5

√√81=⁴√81=3

∛√27²=⁶√(3³)²=⁶√(3²)³=⁶√3⁶=3

∛√4³=⁶√64=2

√∛49³=√49=7

∛⁴√16⁶=¹²√(4²)⁶=¹²√4¹²=4

Answer 2

Oblicz:

a) (√10)² = 10

b) √4¹⁰ = 4^(10/2) = 4^5 = 1024

c) ∛125² =  ∛125 * 125) =  ∛125 *  ∛125 = 5 * 5 = 25

d) ⁵√32³ = ⁵√(32 * 32 * 32) = ⁵√32 * ⁵√32 * ⁵√32 = 2 * 2 * 2 = 8

e) (⁸√625)² = ⁴√625 = ⁴√(5 * 5 * 5 * 5) = 5

f) √√81 = √9 = 3

g) (∛√27)² = (∛(27^1/2))²= (27^1/6)² = 27^1/3 = ∛27 = 3

h) ∛√4³ ∛(√(4 * 4 *4) = ∛(2 * 2 * 2) = 2

i)(√∛49)³ = (√(49^1/3))³ = (49^1/3 : 2)³ = (49^(1/6))³ = 49^(1/2) = √49 = 7

j) ∛⁴√16⁶ = ∛(⁴√(16 * 16 * 16 * 16 * 16 * 16) = ∛(2 * 2 * 2 * 2 * 2 * 2) = 2 * 2 = 4