Show: t(x) = x√2 + √3 is irrational. Hint: consider t(x)² Earlier in the question we were asked to show that the square root of 6 is irrational, which I did. But I can't seem to figure the last part out. I have included an image for reference. 

Help is much appreciated!

Of course you have $$t(x)^2 = 2x^2+2x\sqrt{6}+3.$$ 
Now $x$ is rational but $\sqrt{6}$ is irrational and so what can you conclude about the rationality/irrationality of $t(x)^2$? 
But now suppose $t(x)$ is rational...
