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1)-57 rational or irrational? 2)0.60719001 rational or irrational?3)what is the answer...
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High School Teacher
1) 57 is rational because it has an a finished answer
2) 0.6.... is irrational because it cannot be written as a fraction
4) simplified is 2 times root <94>
Posted by jdkarsten on October 11, 2008 at 12:19 AM (Answer #1)
eNoter, Dean's List
hi this is reallyeasy. -57 is irrational cause it is a negative number. 2.) irrational 3. the root of 384 is 19.595917
Posted by popished on October 25, 2008 at 6:45 AM (Answer #2)
High School Teacher
I agree that rational numbers can be written as the ratio (fraction) of two integers. Irrational numbers are non-repeating, non-terminating. 0.60719001 terminates and can be written as a fraction (although cumbersome) 60719001/100000000.
1/root (121) can be 1/11 OR - 1/11 since 121 has TWO square roots.
Regarding root (384), we can simplify 384 into 4 X 96 (not 94). The radical answer (yes this is irrational, but we are not done yet.) The greatest square factor of 384 is 64. (I kept dividing by 4 until I landed at 6) So we get the square root of 64 times the square root is 6 - or 8Xroot(6)
Posted by dogsg on November 11, 2008 at 9:38 AM (Answer #3)
I though that you are not allowed to ask multiple questions at a time but nevermind, I will still try and help you solve the equation.
1) -57 is rational as it is still a real number, means it is not a complex number that goes on for a few thousands digits. It is a terminating digit, means it will stop in some point of time, it won't carry on forever
2)0.60719901 is a rational number, same as negative 57. The reason is same as the above
3) 1/ sqrt121= positive 1/11 or negative 1/11 as 121 has positve and negative roots
4) sqrt384, according to three significant figures is 19.6. The more complex one is 19.59591794 and so on. It is a complex number and so an irrational number. To change it to surd, divide 384 by 6 to get 64. Then sqrt 64 to get 8. You get surd form (a)sqrt(b) of 8sqrt6, which is the same as sqrt384, but in simpler terms.
Posted by revolution on July 2, 2010 at 6:42 PM (Answer #4)
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