Question

Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth.

Answer 1

@jim_thompson5910

Answer 2

yay! your back :)

Answer 3

let x be the unknown number


x is between 5.2 and 5.5, so,


\[\Large 5.2 < x < 5.5\]


\[\Large (5.2)^2 < x^2 < (5.5)^2\]


\[\Large 27.04 < x^2 < 30.25\]


agreed so far? or no?

Answer 4

yes

Answer 5

what whole number is between 27.04 and 30.25?

Answer 6

28

Answer 7

what is the square root of 28?

Answer 8

5.29150262213

Answer 9

do you agree that 5.29150262213 is between 5.2 and 5.5 ?

Answer 10

yes

Answer 11

is 5.29150262213 rational ? or irrational?

Answer 12

irrational

Answer 13

yep because there is no pattern that repeats. It seems like it's random

so 5.29150262213 can't be written as a fraction of two whole numbers

Answer 14

right!

Answer 15

so by extension, \(\Large \sqrt{28} \) is also irrational

Answer 16

ok so how would we put that answer in a sentence?

Answer 17

just write what I posted but in your own words

Answer 18

um is this a good answer?
An irrational number between 5.2 and 5.5 is 5.29150262213. It is irrational because there is no pattern that repeats and it cant be written as a fraction of two whole numbers.

Answer 19

yes that works

Answer 20

awesome! next! :)

Answer 21

@jim_thompson5910

Answer 22

tell me what you're thinking

Answer 23

i think conner is correct

Answer 24

why

Answer 25

i dont know.. lol

Answer 26

can you tell me..

Answer 27

this might help

http://www.onlinemathlearning.com/image-files/387x248xari121.gif.pagespeed.ic.vFV2Lan_oa.png

Answer 28

ok do you know the answer?

Answer 29

yes but you should look at the link

Answer 30

ok i saw it :)

Answer 31

what is 2^7 times 2^9 equal to

write it in exponential form

Answer 32

65536

Answer 33

write it in exponential form

Answer 34

example: 32 in exponential form is 2^5

Answer 35

i what 65536 is though in exponential form

Answer 36

i dont know*

Answer 37

hint: rule 1 in that link

Answer 38

i dont get it

Answer 39

example:

7^5 times 7^8 = 7^(5+8) = 7^13

Answer 40

but 65536 is a long number.. can you wirte it in exponential form for me..

Answer 41

@jim_thompson5910

Answer 42

use my last example to do 2^7 times 2^9