Question

Want a new fan and medal? Just help with practice.


http://static.k12.com/bank_packages/files/media/fddea5ba9e8b840082f48ed794271c2c.png

Rational or irrational?

Answer 1

rational

Answer 2

http://static.k12.com/bank_packages/files/media/d961ed1a5e5640f11b592a1c80383a22.png
Rational or irrational?

Answer 3

9

Answer 4

yes, whenever you have a square root of a perfect square,
(or a cube root of a perfect cube, and such....)

then THAT is a rational number

Answer 5

Thank-you. So rational?

Answer 6

yes

Answer 7

1 or 2

Answer 8

and, this is an identifiable pattern.

Such as,
\(\large\color{black}{ \displaystyle \sqrt[n]{a^n}\in{\bf R} }\) where \(\large\color{black}{ \displaystyle \left\{ n\in {\bf Z}\right\} }\)

Answer 9

R is a notation for a set of all rational numbers.
Z is a notation for a set of all integers.

and \(\large\color{black}{ \displaystyle \in }\) symbol means "belongs to the set of"

Answer 10

so, this \(\large\color{black}{ \displaystyle \sqrt[n]{a^n} }\) (nth root of a^n) is a rational number.

Answer 11

you're talking about number 2 correct?

Answer 12

For example, \(\large\color{black}{ \displaystyle \sqrt[3]{27} }\) because really, it is \(\large\color{black}{ \displaystyle \sqrt[3]{3^3} }\) , and that is just \(\large\color{black}{ \displaystyle 3}\) .

Answer 13

this is all about number 1 and 2

Answer 14

but, 84 is not a perfect square (for #2)

Answer 15

oh. 1 is rational 2 is rational.

Answer 16

yes

Answer 17

2. irrational?

Answer 18

yes, I thought you said irrational for nuber 2

Answer 19

I was s thinking about how irrational it is. Sorry.

Answer 20

1. rational
2. Irrational

Answer 21

http://static.k12.com/bank_packages/files/media/3df83141d56cf05c0baa175a25f45b86.png .I think its irrational.

Answer 22

yes

Answer 23

because 121 is a square root of 11 and 144 is a square root of 12

Answer 24

and my bad about notations R denotes all real numbers, and Q denotes rational numbers.

Answer 25

Its okay. one more. http://static.k12.com/bank_packages/files/media/af2a1efbf07da0dfa303680f910f7a1c.png 100% sure its rational.

Answer 26

and thence any irrational numbers x would have a notation,
\(\large\color{black}{ \displaystyle \left\{x:x\cancel{\in} {\bf Q},x\in{\bf R} \right\}}\)

yes this one is rational

Answer 27

it is equal to 20
(but do not say Plus-minus 20)

Answer 28

Yay! Thank-you for the huge help and understanding.

Answer 29

(by definition a square root is a positive, unless dealing with quadratics or other equations of even powers)

Answer 30

alright ... good luck!