## becca9898 one year ago Is the square root of 5 rational or irrational? I want to say rational?

1. zepdrix

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

2. 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 $$\large\rm \frac{0}{1}$$.

3. zepdrix

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

4. zepdrix

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

5. zepdrix

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

6. becca9898

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

7. Hero

The square root of a prime number is irrational

8. becca9898

Thank you guys!

9. 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.