Question

The square root of two is a rational number? thank you

Answer 1

Is it True or False? If so it is False.

Answer 2

I don't like just giving wiki references, but I really don't what to say about the answer to this question since it is so straight-forward
http://en.wikipedia.org/wiki/Irrational_number

Answer 3

can it be expressed as the quotient of two integers?

Answer 4

well its a square root and I got 1.4142 and I know that 2 is a rational number?

Answer 5

the square root of a number is rational only if the numbers under the sign are perfect squares
for instance\[\sqrt{\frac94}=\frac{\sqrt9}{\sqrt4}=\frac32\]so it is rational, because 4 and 9 are perfect squares
is 2 a perfect square?

Answer 6

yes it is

Answer 7

then what number times itself equals 2?
if you can find a whole number that \(times\) \(itself\) equals 2, then 2 is a perfect square

Answer 8

so the square root of 2 is true

Answer 9

there is no whole number that times itself equals 2
1x1=1
so no
2x2=4
which is bigger than 2
from there (3x3, 4x4, etc.) all that will only be bigger than 2
hence there is no whole number that times itself equals 2
so \[\sqrt2\] is irrational

Answer 10

thank you so very much for helping me and teaching me I understand it a whole lot better thank you