Răspuns:
Explicație pas cu pas:
1 a)
3√2 + √18 - √50 = 3√2 + 3√2 - 5√2 = 6√2 - 5√2 = √2
b)
√27 + 2√3 - √75 = 3√3 + 2√3 - 5√3 = 5√3 - 5√3 = 0
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2. a)
√12/49 - √27/25 + √48/121 = 2√3/7 - 3√3/5 + 4√3/11
= 110√3/385 - 231√3/385 + 140√3/385 = 19√3/385
b)
4√2/√27 + 2√2/√27 - 5√2/4√3 = 6√2/3√3 - 5√2/4√3
= 24√2/12√3 - 15√2/12√3 = 9√2/12√3 = 3√2/4√3 = 3√6/12 = √6/4
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3a)
√2 = 1*√2
√6 = √2*√3
√12 = √3*√4
......
√9900 = √99*√100
b)
(1 - √2)/√2 = 1/√2 - √2/√2 = 1/√2 - 1
(√2 - √3)/√6 = 1/√3 - 1/√2
(√3 - √4)/√12 = 1/√4 - 1/√3
........
(√99 - √100)/√9900 = 1/√100 - 1/√99
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1/√2 - 1 + 1/√3 - 1/√2 + 1/√4 - 1/√3 + ....+ 1/√100 - 1/√99
= 1/√100 - 1 = 1/10 - 1 = -9/10
