anonymous
  • anonymous
Which of the following numbers is irrational? negative 7 over 4, 2 over 3, square root of 3, square root of 4 a fraction with numerator negative 7 and denominator 4 a fraction with numerator 2 and denominator 3 square root of 3 square root of 4
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
help
UsukiDoll
  • UsukiDoll
\[\LARGE -\frac{7}{4}, \frac{2}{3}, \sqrt{3},\sqrt{4}\] like this?
anonymous
  • anonymous
yes @UsukiDoll

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UsukiDoll
  • UsukiDoll
ok the definition of a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero. Since q may be equal to 1, every integer is a rational number.
UsukiDoll
  • UsukiDoll
irrational numbers can't be expressed as fractions. having square roots is a dead giveaway of an irrational number
UsukiDoll
  • UsukiDoll
an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals.
UsukiDoll
  • UsukiDoll
\[\LARGE e, \pi, \sqrt{2}\] are examples of irrational numbers.
UsukiDoll
  • UsukiDoll
so from this list \[\LARGE -\frac{7}{4}, \frac{2}{3}, \sqrt{3},\sqrt{4} \] which of them are irrational?
anonymous
  • anonymous
3
UsukiDoll
  • UsukiDoll
yes the square root of 3 is irrational
UsukiDoll
  • UsukiDoll
the square root of 4 can be simplified further into 2 and it's rational because it can be expressed as a fraction which is \[\LARGE \frac{2}{1}\]
UsukiDoll
  • UsukiDoll
\[\LARGE \frac{2}{1} \rightarrow 2 \]
UsukiDoll
  • UsukiDoll
everything else is rational \[\LARGE \sqrt{3} \] is irrational.
anonymous
  • anonymous
thanks :) @UsukiDoll

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