week4, Pre-cal11

this week, I learnt the new knowledge, the way to adding & subtracting the radical expression.

There are some rules in there

  1. the radicals can just be adding or subtracting between the like terms, such as,                     the 2 \sqrt{2} – 3\sqrt{2} = –\sqrt{2}. and it works when, \sqrt{2}+\sqrt{8}=3\sqrt{2},                                                                    because the \sqrt{8}=2\sqrt{2}   therefore, the first step for the adding or subtracting’s question is always to check, is there any term could be further simplify to be the same term as others obviously.

2. if the question is seem like that \sqrt{2}\sqrt{5}, the terms cannot be further simplified because \sqrt{2} is the unlike terms with \sqrt{5}. people cannot just do the math under the radical symbol, as to do the math as 2+5=7 , and use these methods to determine the answer is \sqrt{7}.

3. there are always the track in there, such as \sqrt{2} +\sqrt[3]{2}=?   be careful with the whole radicals, not only the radicands, the index also determines two radicals are the like terms or not. thus, the questions can not have a simplified sum, it just stop there.

the radicals just could be + or – between the like terms, (same radicands and index)

COULD you do the question?

Ex: –\sqrt[3]{2}+\sqrt[3]{8}+\sqrt[3]{32}\sqrt{4} +\sqrt{16}

 

answer:

  1. = –\sqrt[3]{2}+2 +2\sqrt[3]{3} -2 +4
  2. =-\sqrt[3]{2}+2\sqrt[3]{3}+4

 

 

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