Question

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

Answer 1

Answer:

Your answer is here:

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+3√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 a irrational number.

This is a contradiction.

This contradiction is arisen as our assumption is wrong.

Hence (√3+√5)^2 is an irrational number.

Marks brainiest.

☺️☺️☺️☺️☺️