question (1 Viewer)

[mmmmmmmmaaaaaaa]

Screenshot isn't working for some reason

to prove sqrt(4n-2) is irrational
can I take out sqrt2 as a factor to be sqrt2 * sqrt(2n-1) and then show sqrt(2) is irrational by proof of contradiction to show sqrt(4n-2) is irrational

ie if sqrt(2) is irrational then
sqrt2 * sqrt(2n-1) is irrational and
sqrt(4n-2) is irrational

Proof solved

Would this logic work and would I receive full marks for this?

 

[cossine]

Screenshot isn't working for some reason

to prove sqrt(4n-2) is irrational
can I take out sqrt2 as a factor to be sqrt2 * sqrt(2n-1) and then show sqrt(2) is irrational by proof of contradiction to show sqrt(4n-2) is irrational

ie if sqrt(2) is irrational then
sqrt2 * sqrt(2n-1) is irrational and
sqrt(4n-2) is irrational

Proof solved

Would this logic work and would I receive full marks for this?

So irrational * irrational can equal a rational number so no it will not work. e.g. 1/sqrt(2) * sqrt(2)