Question

Which of the following are rational numbers?
A; √3/27
B; 3-27 (I already know this one is rational)
C; √3 - √27
D; √3/ √27
E; ( √27+3)( √27-3)

Answer 1

some gimmick here
\[\frac{\sqrt{3}}{\sqrt{27}}=\sqrt{\frac{3}{27}}=\sqrt{\frac{1}{9}}\]

Answer 2

which as you can see is \(\frac{1}{3}\) so pick that one for sure

Answer 3

try multiplying out
\[(\sqrt{27}+3)(\sqrt{27}-3)\] and see what you get

Answer 4

So √3/√27 = 1/9 ?

Answer 5

no it is \(\frac{1}{3}\)

Answer 6

since the square root of 9 is 3

Answer 7

oh ok. and (√27+3)(√27-3) = 39.5884572681199

Answer 8

it is
\[27-9=18\]

Answer 9

how?

Answer 10

\[(a+b)(a-b)=a^2-b^2\]

Answer 11

and so
\[(\sqrt{27}+3)(\sqrt{27}-3)=27-9\]

Answer 12

ok i kind of understand. is that all?

Answer 13

yeah i think that is all the rationals ones