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1)-57 rational or irrational? 2)0.60719001 rational or irrational?3)what is the answer...

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maganda123 | eNoter

Posted October 9, 2008 at 3:47 PM via web

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1)-57 rational or irrational? 2)0.60719001 rational or irrational?3)what is the answer to this:<1/root 121>4)what is the root of 384?

these are math questions. please help me answer.there are 4 questions.

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jdkarsten | High School Teacher | eNotes Newbie

Posted October 11, 2008 at 12:19 AM (Answer #1)

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1) 57 is rational because it has an a finished answer

2) 0.6.... is irrational because it cannot be written as a fraction

3) 1/11

4) simplified is 2 times root <94>

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popished | Student , Grade 10 | eNoter

Posted October 25, 2008 at 6:45 AM (Answer #2)

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hi this is reallyeasy. -57 is irrational cause it is a negative number. 2.) irrational 3. the root of 384 is 19.595917

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dogsg | High School Teacher | (Level 2) Adjunct Educator

Posted November 11, 2008 at 9:38 AM (Answer #3)

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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)

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revolution | College Teacher | Valedictorian

Posted July 2, 2010 at 6:42 PM (Answer #4)

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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.

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