Question

Show that ( √3+√5)^2 is an irrational number ?​

Answer 1

Answer:

2+2+2+2+2+2×2+2+2+2+2+2=75747565656

Answer 2

Let us assume to the contrary that (√3+√5)² is a rational number,then there exists a and b co-prime integers such that,
(√3+√5)²=a/b

3+5+2√15=a/b

8+2√15=a/b

2√15=(a/b)-8

2√15=(a-8b)/b

√15=(a-8b)/2b
(a-8b)/2b is a rational number.
Then √15 is also a rational number
But as we know √15 is an irrational number.
This is a contradiction.
This contradiction has arisen as our assumption is wrong.
Hence (√3+√5)² is an irrational number.