Question

The number (√3 + √5)x(√3 + √5) is *​

Answer 1

Answer:

hope it helps you

Step-by-step explanation:

What would you like to ask?

10th

Maths

Real Numbers

Revisiting Irrational Numbers

Show that (√(3)+√(5))2 is ...

MATHS

Show that (3+5)2 is an irrational no.

EASY

Share

Study later

ANSWER

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.