Question

Sa se simplifice expresiile:
$\sqrt[10]{ 2^{5} }$ ; $\sqrt[12]{ (-5)^{4} }$ ; $\sqrt[8]{ a^{4} }$ ; $\sqrt{ \frac{625}{256} }$ ; $\sqrt[6]{ ( \sqrt{7}-2) ^{3} }$ ; $\sqrt[4]{(1- \sqrt{2})^2 }$ ; $\sqrt[9]{( \sqrt{3}- \sqrt{5})^3 }$ ; $\sqrt[10]{( \sqrt{3}-4)^2 }$ ; $\sqrt[6]{(1- \sqrt{2})^2 }$

Answer 1

  ¹⁰√2⁵  = 2⁵ /¹⁰ = 2 ¹/² = √2 
( -5)⁴ = 5⁴ 
¹²√5⁴ = 5 ⁴/¹² = 5¹/³ = ∛5
⁸√a⁴ = a⁴/⁸  = a¹ /² = √a
√625 / √256 = 25 /16 
√7 - 2 > 0 
⁶√(√7-2)³ = (√7 -2) ³/⁶= (√7 -2) ¹/²= rad( √7 - 2) 
1 - √2 < 0 
⁴√(1-√2)² = ⁴√(√2-1)² = ( √2 -1) ²/⁴ = (√2 -1) ¹/² = rad( √2 -1) 
⁹√ (√3 - √5)³  = (√3 - √5)³/⁹   = ( √3  - √5 )¹/³ = rad.∛(√3 - √5)
√3 - 4  < 0 
¹⁰√( 4 -√3)² = (4 - √3)²/¹⁰ = ( 4 - √3)¹ /⁵ = rad.⁵√(4 - √3)
1 - √2 < 0 
⁶√(√2-1)² = (√2-1) ²/⁶ = ( √2 - 1  )¹/³ = rad.∛(√2-1)