Question

prove that ✓3+✓5 is irrational​

Answer 1

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 2

Step-by-step explanation:

Then √15 is also a rational number. But this contradicts the fact that √15 is an irrational number. √3 + √5 is an irrational number. Hence, proved.