Esercizi sui radicali

Esercizi sui radicali

di Mattia Puddu

Calcola le seguenti somme algebriche di radicali, supponi positivi i radicandi letterali.

1. 11sqrt(5) + 6sqrt(2) - (8sqrt(5) + 3sqrt(2)) =

= 11sqrt(5) + 6sqrt(2) - 8sqrt(5) - 3sqrt(2) = 3sqrt(5) + 3sqrt(2) = 3(sqrt(5) + sqrt(2))

2. 5sqrt(3) + 3sqrt(7) - [2sqrt(3) - (4sqrt(7) - 3sqrt(3))] =

= 5sqrt(3) + 3sqrt(7) - 2sqrt(3) + 4sqrt(7) - 3sqrt(3) = 7sqrt(7)

3. 3sqrt(48) + 2sqrt(32) + sqrt(98) - (4sqrt(27) + sqrt(450)) =

= 3sqrt(2⁴ * 3) + 2sqrt(2⁵) + sqrt(2 * 7²) - 4sqrt(3³) - sqrt(2 * 5² * 3²) = 12sqrt(3) + 8sqrt(2) + 7sqrt(2) - 12sqrt(3) - 15sqrt(2) = 0

4. 2 cubert(54) - fourthroot(243) + 3 fourthroot(48) - cubert(250) =

= 6cubert(2) - 3fourthroot(3) + 6fourthroot(3) - 5cubert(2) = cubert(2) + 3fourthroot(3)

5. 2sqrt(27/8) + 5sqrt(3/50) + 7sqrt(27/98) - 5sqrt(147/50) =

= 3sqrt(3/2) + 3sqrt(3/2) + 3sqrt(3/2) - 7sqrt(3/2) = 0

6. sqrt(75) + 3sqrt(18) - 2sqrt(12) - 2sqrt(50) =

= 5sqrt(3) + 9sqrt(2) - 4sqrt(3) - 10sqrt(2) = sqrt(3) - sqrt(2)

7. 3sqrt(128) - 2sqrt(72) - (2sqrt(50) + sqrt(8)) =

= 24sqrt(2) - 12sqrt(2) - 10sqrt(2) - 2sqrt(2) = 0

8. sqrt(a³) - 3a²sqrt(a) + 2a²sqrt(a) =

= a sqrt(a) - 3a²sqrt(a) + 2a²sqrt(a) = (a - a²)sqrt(a) = a(1 - a)sqrt(a)

9. sqrt(a⁵) - 3a²sqrt(a) + 2a²sqrt(a) =

= a²sqrt(a) - 3a²sqrt(a) + 2a²sqrt(a) = 0

10. 5/4 sqrt(a) - 1/2 sqrt(b) + 3/4 sqrt(b) - 2/8 sqrt(a) =

= ((10 - 2)/8)sqrt(a) - ((2 - 3)/4)sqrt(b) = sqrt(a) + 1/4sqrt(b)