SOLUTION: How do I add or subtract irrational numbers? e.g {{{ 19sqrt(2)-6sqrt(2) }}} I have been told it is the same as rational numbers but do not understand this

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Question 469802: How do I add or subtract irrational numbers?
e.g +19sqrt%282%29-6sqrt%282%29+
I have been told it is the same as rational numbers but do not understand this
Found 2 solutions by bucky, kingme18:
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
For your particular problem, it is possible to subtract these two terms because the quantity under the square root sign is the same for both terms.
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For this problem, you can think of it this way:
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You were given:
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19%2Asqrt%282%29-6%2Asqrt%282%29
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Since sqrt%282%29 is common to both terms, you can factor it out. In factored form your problem becomes:
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%2819+-+6%29%2Asqrt%282%29
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Now combine the two numbers inside the parentheses, that is subtract 6 from 19 and you get:
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13%2Asqrt%282%29
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and this is the answer to the subtraction problem that you started with.
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Remember, this method of combining (adding or subtracting) is only possible if the irrational terms are the same. If your original problem had been:
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19%2Asqrt%282%29+-+6%2Asqrt%283%29
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then you could not combine the two terms using addition or subtraction. You can recognize this by the fact that you cannot factor out the irrational radicals because they are different in each of the two terms.
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Hope this helps you understand the addition and subtraction process for irrational numbers a little better. Once you get used to ensuring that terms in the radicals are the same, you will just be able to say "19 times the square root of two minus 6 times the square root of 2 is 13 times the square root of two without wasting time by going through the factoring process. I just showed you the factoring in hopes that it would help you understand what is going on in the problem a little better. Good luck.


Answer by kingme18(98) About Me  (Show Source):
You can put this solution on YOUR website!
As long as the irrational number is EXACTLY the same, it's like with variables: 19x-6x=13x. If you have 19 "square root of 2"s, and you subtract 6 "square root of 2"s, you still have 13 "square root of 2"s: +19sqrt%282%29-6sqrt%282%29=13sqrt%282%29+


If it wasn't the same irrational number, like +19sqrt%282%29-6sqrt%283%29+, then they're not like terms. That would be like 19x-6y, which you can't combine. However, some radicals can be simplified so that the irrational numbers DO match. It doesn't sound like you're at that point just yet, so I won't go into detail. Just remember: adding and subtracting radicals (irrational numbers) is just like adding and subtracting variables: you can combine them if they're like terms.