Prove that √3+√5 is an irrational number

1.	Prove that √3+√5 is an irrational number
Answer» ONG>Answer: Let √3 + √5 be a RATIONAL NUMBER , say r then √3 + √5 = r On SQUARING both sides, (√3 + √5)2 = r2 3 + 2 √15 + 5 = r2 8 + 2 √15 = r2 2 √15 = r2 - 8 √15 = (r2 - 8) / 2 Now (r2 - 8) / 2 is a rational number and √15 is an irrational number . SINCE a rational number cannot be equal to an irrational number . Our assumption that √3 + √5 is rational wrong .

Answer» ONG>Answer:

Let √3 + √5 be a RATIONAL NUMBER , say r

then √3 + √5 = r

On SQUARING both sides,

(√3 + √5)2 = r2

3 + 2 √15 + 5 = r2

8 + 2 √15 = r2

2 √15 = r2 - 8

√15 = (r2 - 8) / 2

Now (r2 - 8) / 2 is a rational number and √15 is an irrational number .

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

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