Question

Find a counterexample.
The square root of a number x is always less than x.

Answer 1

what aobut numbers less than 1 but greater than 0?

Answer 2

thats the thing, like which ones

Answer 3

i believe all of them

Answer 4

ok what if x= .25 or 1/4

Answer 5

like this... or what

Answer 6

\[\sqrt{.25}\]
this is easier

Answer 7

oh ok thanks. can i ask you one more question?

Answer 8

shoot

Answer 9

Describe a pattern in the sequence below. Predict the next number.
256, 16, 4, 2, . . .

Answer 10

ok, what's the square root of 256?

Answer 11

16

Answer 12

and the square root of 16?

Answer 13

4

Answer 14

ok then the next term will be the square root of 2 right?
and dont bother writing it in decimal form
the square root of 2 is nonterminating

Answer 15

i mean irrational

Answer 16

oh ok because i kept looking for the square root and i couldn't find it

Answer 17

its one of the 2

Answer 18

\[\sqrt{2}\]
and the next term will be \[\sqrt{\sqrt{2}}\]