Question

21 Освободитесь от иррациональности в знаменателе дроби. 1)√2/5√3 2)√5+2/√5-2 3) 17/3√2+1 4) 4/2√5√12 5) 7/√18+2√2+1​

Answer 1

Ответ:

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Объяснение:

1) √2/5√3 = √2/5√3 * √3/√3 = √6/15

2) √5+2/√5-2 = (√5+2)(√5+2)/(√5-2)(√5+2) = (5+4√5+4)/(5-4) = (9+4√5)/1 = 9+4√5

3) 17/3√2+1 = 17/3(√2+1) * (√2-1)/(√2-1) = 17(√2-1)/3(2-1) = 17(√2-1)/3

4) 4/2√5√12 = 4/2(√5*√12) = 4/2(√60) * (√60)/(√60) = 4√60/120 = √60/30

5) 7/√18+2√2+1 = 7/√(18+4√8+1) = 7/√(9+4√8+9) = 7/√(18+4√8+9) * (√(18+4√8)-3)/(√(18+4√8)-3) = 7(√(18+4√8)-3)/((18+4√8)-9) = 7(√(18+4√8)-3)/9