Question

Is the square root of 5 rational or irrational?

I want to say rational?

Answer 1

A rational number looks like this: \(\large\rm \frac{a}{b}\) where a and b are whole numbers and b is not zero.

Answer 2

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 \(\large\rm \frac{0}{1}\).

Answer 3

\(\large\rm \sqrt{16}\) is rational because I can write it as \(\large\rm \frac{4}{1}\)

Answer 4

But \(\large\rm \sqrt{17}\) is `not` rational.
There is no nice representation with integers for this number :(

Answer 5

Any ideas for the sqrt(5)? :)
Does this give you any hints?

Answer 6

I would say then it would be irrational because there is no representation?

Answer 7

The square root of a prime number is irrational

Answer 8

Thank you guys!

Answer 9

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.