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Răspunsuri la întrebare
E1.
a ) √625×81×361
√625 √81 √361
√25² √9² √19²
25 × 9 × 18
225 × 19 = 4275
b ) ³√27 × 4⁶
³√27 ³√4⁶
³√3³ × 4²
3 × 4²
4² = 4 × 4 = 16
3 × 16 = 48
c ) ³√2¹² × 3‐⁶
³√2¹² ³√3‐⁶
2⁴ × 3‐²
2⁴ = 2 × 2 × 2 × 2 = 16
16 × 3‐²
16 × 1 / 3²
3² = 3 × 3 = 9
16 × 1 / 9
16 / 1 × 1 / 9
16 × 1 / 1 × 9
16 / 1 × 9 = 16 / 9
d ) ³√343² × 21‐⁶
³√343² × 1 / 21⁶
343² × 1 / 21⁶
343² / 21⁶
³√343² / 21⁶
³√343² / ³√21⁶
³√343² / 21²
³√343² / 21² = 21² = ( 3 × 7 ) ² = 3² × 7²
³√7³
7² / 3² × 7²
3 × 3 = 9
7² / 9 × 7²
1 / 9
E2.
a ) √784 / 1225
784 : 49 / 1225 : 49
16 / 1225 : 49
16 / 25
√4² / √25
√4² / √5²
4 / √5²
4 / 5
b ) ³√ - 125/ 64
‐ ³√125 / 64
‐³√125 / ³√64
³√5² / ³√64
³√5² / ³√4³
‐ 5 / ³√4³
‐5 / 4
c ) √1 / 6⁴ × 81 / 625
1 / 6² × 9 / 25
1 / 36 × 9 / 25
1 / 4 × 1 / 25 = 1 / 100
d ) - √216 / 343 × 1331 / 8
√‐27 / 343 × 1331
√‐35937 / 343 = nedefinit.
sau
- √216 / 343 × 1331 / 8
√‐27 / 343 × 1331
√ ‐35937 / 343
√35937 / 343 i
√35937 / √343 × i
33√33 / 7√7 × i
33√231 / 49 × i
- 33√231 / 49 i
e ) ³√√729 × 81³ / 64² × 8⁴
⁶√729 × 81³ / 64² × 8⁴
⁶√9³ × 9⁶ / 8⁴ × 8⁴
6√9⁹ / ⁶√8²
√9³ / ³√8⁴
√9³ / ³√8⁴
3³ / 2⁴ = 27 / 16
E3.
a ) ³√2⁶ = 2² = 4
b ) ³√( 1/2) ² ⁶
( ( 1/2 ) ² ) ⁶
( 1/2 ) ⁴ = 1/16
c ) √(3/5)² -⁴
( ( 3/5 )² )‐⁶
( 3/5 ) ‐⁴
( 5/3 )⁴ = 625/81
d ) ³√4√256
³√4 × 256
³√64 = 4
e ) √√1296x⁸y¹²
√36x⁴y⁶ = 6x²y³