## anonymous one year ago Which of the following is a rational number? square root 97square root 98, square root 99, square root 100 square root 97 square root 98 square root 99 square root 100

1. UsukiDoll

a rational number can be expressed as a fraction an irritation number can't be expressed as a fraction

2. UsukiDoll

*irrational

3. UsukiDoll

examples of rational numbers $\LARGE \frac{1}{2}, \frac{3}{1}$ Examples of irrational numbers $\LARGE \pi, e, \sqrt{3}$

4. UsukiDoll

let's start with the last one. what is the square root of 100?

5. anonymous

10 @UsukiDoll

6. UsukiDoll

yay so that's a rational number. I can express that as a fraction which is $\large \frac{10}{1}$

7. anonymous

right @UsukiDoll

8. UsukiDoll

I don't think there are any more choices for rational numbers... 97 is a prime number and that's in a square root . that's irrational

9. UsukiDoll

and even if we did simplify the square root of 98 and 99, we will still have a square root left order...

10. anonymous

so 97s the awnser @UsukiDoll

11. UsukiDoll

no for 2 reasons 97 is a prime number 97 is inside the square root and can't be expressed as a fraction .

12. UsukiDoll

but not all square roots are irrational ... so we need to be careful on this. if we are left with a square root that can be simplified further .. it becomes rational

13. UsukiDoll

for example $\LARGE \sqrt{2}$ is irrational but $\LARGE \sqrt{4}=2$ is rational

14. UsukiDoll

there could be some more rational numbers lurking

15. UsukiDoll

or not...

16. UsukiDoll

|dw:1438236905176:dw| take the square root of 49 and square root of 9

17. UsukiDoll

even if I do take those square roots, I still have something left over and they are irrational.

18. UsukiDoll

|dw:1438237057661:dw| I can't express these as fractions ... so again they are in the irrational group

19. UsukiDoll

but for the last one which is square root of 100 I can express it as a fraction, so that's the rational number we are looking for |dw:1438237176763:dw|

20. sepeario

* a rational number can be expressed as a fraction of two whole numbers.