Which of the following is not a rational number?a) 25 b) 45 c) 256 225 d) 3 4

Question

Which of the following is not a rational number?a)       25  b)       45  c)             256      225      d)       3    4

Skye Hamilton · Accepted Answer

Step 1So       3    2   is a rational number, but in the definition it does not say that       p    q   should be an integer, only that both of p and q should. Rational numbers can have decimals and even an infinite decimals, BUT any rational number&#039;s decimals will have a repeating pattern at some point whether it be like      2    3    =  0.666...or      92    111000    =  0.000    828    828    828...or      3    2    =  1.500    000    000...The reason why       45   is not rational is not because it has decimals. We have that      45    =      5    ⋅    9    =      5        9    =  3      5    ,so       45   must be irrational if       5   is irrational. In fact it is known that       p   for all primes p is irrational such as   p  =  5 Therefore we can say that       45   is irrational.

Kendra Hudson · Accepted Answer

Step 13 out of the 4 options on that exam can be written in       p    q   form, where p and q are integers. Note that integers can not have decimals. For example:a)       25    =  5  =      5    1  b)       45    =      ?    ?  c)             256      225        =            256              225        =      16    15  d)       3    4  So a, c, and d can be written in       p    q   form (5,1,16,15,3,4 are all integers) but b cannot. If you think b is rational, then fill in the two question marks with integers and you will find that you cannot.

Which of the following is not a rational number? a) sqrt(25) b) sqrt(45) c) sqrt((256)/(225)) d) 3/4

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