Proving Irrationality: Is sqrt2 + sqrt5 + sqrt7 Rational or Irrational?

[hew]

Homework Statement

decide if sqrt2 + sqrt5 +sqrt7 is rational or irrational, with proof

Homework Equations

The Attempt at a Solution

i assumed that it was rational, the equation =r
sqrt2 + sqrt 5=r- sqrt7
7 + 2sqrt10=r^2 + 7 -2r*sqrt7
2sqrt10=r^2 -2r*sqrt7
could i have a hint on how to rearrange this, i have already proved in an earlier question that sqrt2, sqrt5, sqrt7 are irrational

thankyou

 

[Office_Shredder]

You're almost there. square both sides again, and you can write sqrt(7) as a linear combination of rational numbers. i.e. you've shown sqrt(7) is rational.