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Before starting:
(√a)² = √a √a = a
√(a²) = IaI
√(ab) = √a √b
√(a/b) = (√a) / (√b)
√(a + b) ≠ √a + √b
= √20 + √45 - √5
= √(4 5) + √(9 5) - √5
= [(√4) (√5)] + [(√9) (√5)] - √5
= [(√2²) (√5)] + [(√3²) (√5)] - √5
= [2 (√5)] + [3 (√5)] - √5
= 2√5 + 3√5 - √5
= 5√5 - √5
= 4√5 → first answer
= 9^(1/3) 81^(1/3) → you know that: 81 = 9² = 9 9 = 3² 3² = 3^4
= (3^2)^(1/3) (3^4)^(1/3) → you know that: (x^a)^b = x^(ab)
= 3^[2 (1/3)] 3^[4 (1/3)]
= 3^(2/3) 3^(4/3) → you know that: x^(a) * x^(b) = x^(a + b)
= 3^[(2/3) + (4/3)]
= 3^[(2 + 4)/3]
= 3^[6/3]
= 3^2
= 9 → second answer
