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Dимасuk

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Решение.
В (в) и (г) изменены знаки и степени для получения рационального значения.

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oganesbagoyan

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а)   (312+313)² =625² =((25)²)² = 25⁴ ; (25⁴ ) ^1/4  = 25.
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б)   = ∛(1987 -987)³ =  ∛1000³ =1000.
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в) = ((800 -175)² ) ^(1/4) = (625)² ^ 1/4 =(25⁴ ) ^ 1/4 =25^(4*1/4) =25^1=25.
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г) !  ∛(789³ +3*789²*211+3*789*211²)+ 211³)= ∛(789 +211)³ =∛1000³ =1000.
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д) = ((2002 +498)²) ^ (1/4) = (2500²) ^ (1/4) = ((50²)²) ^(1/4)=(50⁴ ) ^(1/4) =50 .
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е)  =∛(2001 -189)³ = ∛1812³ =1812.
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ж) = ( (2001 - 401)² ) ^ (1/4) =((1600)² )^(1/4 )= ((40²)²)^(1/4) =(40⁴)^(1/4) =40.
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3) =∛(1799+203)³ = 1799+203= 2002.

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символично :(a±b)² =a² ±2ab+b² ; (a±b)³ =a³ ±3a²b +3ab² ±b³ .

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