Question

Prove that 3 + √5 is an irrational number​

Answer 1

Answer:

⇒ 3 + 5 = p q , where p and q are the integers and q ≠0. Since p , q and 3 are integers. So, p - 3 q q is a rational number. ... Hence, is an irrational number.

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Answer 2

Step-by-step explanation:

If ✓5 is irrational.

✓5 = a/b. (assume )

✓5*b = a

✓ 5b = a

By squaring both sides

(✓5b²) = (a²)

5b² = a

Now take a= (5a1)²

5b² = (5a1)²

5b² = 25a1²

b² = 25a1² / 5

b² = 5a1²

= 5 is factor of both a and b.

i.e. ✓5 is irrational number.

so, 3 +✓5 is also irrational.