What is the simplest form of the expression? sqrt 20+ sqrt 45 - sqrt 5

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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

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