Question

5. (2 + sqrt(3) + sqrt(5)) is :(a) a rational number(b) a natural number (c) a integer number (d) an irrational number​

Answer 1

Answer:

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Step-by-step explanation:

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.

Answer 2

Answer:

2+√3+√5 is an irrational number