Mathematics
Joanne123love
19

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

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(1) Answers
hanan1

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions. 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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