prove root 3 and root 5 irrational

1.	prove root 3 and root 5 irrational
Answer» Let√3 +√5 be a rational number , say r then√3 +√5 = r On squaring both sides, (√3 +√5)^2= r^2 3 + 2√15 + 5 =r^2 8 + 2√15 =r^2 2√15 =r^2 - 8 √15 = (r^2- 8) / 2 Now (r^2- 8) / 2 is a rational number and√15is anirrational number . Since a rational number cannot be equal to an irrational number . Our assumption that√3 +√5 is rational wrong .

Answer»

Let√3 +√5 be a rational number , say r

then√3 +√5 = r

On squaring both sides,

(√3 +√5)^2= r^2

3 + 2√15 + 5 =r^2

8 + 2√15 =r^2

2√15 =r^2 - 8

√15 = (r^2- 8) / 2

Now (r^2- 8) / 2 is a rational number and√15is anirrational number .

Since a rational number cannot be equal to an irrational number . Our assumption that√3 +√5 is rational wrong .

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