becca9898
  • becca9898
Is the square root of 5 rational or irrational? I want to say rational?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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zepdrix
  • zepdrix
A rational number looks like this: \(\large\rm \frac{a}{b}\) where a and b are whole numbers and b is not zero.
zepdrix
  • zepdrix
Here are a few examples of rational numbers: \(\large\rm \frac{5}{3}\) is a rational number. \(\large\rm 2\) is a rational number because I can write it as \(\large\rm \frac{2}{1}\). \(\large\rm 0\) is rational because I can write it as \(\large\rm \frac{0}{1}\).
zepdrix
  • zepdrix
\(\large\rm \sqrt{16}\) is rational because I can write it as \(\large\rm \frac{4}{1}\)

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zepdrix
  • zepdrix
But \(\large\rm \sqrt{17}\) is `not` rational. There is no nice representation with integers for this number :(
zepdrix
  • zepdrix
Any ideas for the sqrt(5)? :) Does this give you any hints?
becca9898
  • becca9898
I would say then it would be irrational because there is no representation?
Hero
  • Hero
The square root of a prime number is irrational
becca9898
  • becca9898
Thank you guys!
zepdrix
  • zepdrix
Yay good job becca \c:/ Another way to think about it, only the `perfect squares` are going to be rational when placed under a root. So square root of 4, 9, 16, 25, 36 and so on... these are are rational numbers. All of the roots between them are not.

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