Question

Prove that 5 root3 is irrational ?
Solution
a and b are coprime integer
5 root3 =a/b
Root3=a/b
Root 3 =a/5b
Here a, b and 5 are integers a/5b is rational

Here contradicts occur that root3 is irrational number

Answer 1

Answer:

√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:

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Step-by-step explanation:

This is very easy You have to solve it by contradictory method. You have to prove ur statement wrong in this question Let if possible 7√5 is a rational number =7√5=a/b =√5=a/5b both a and b are integers so that a/5b is rational and so √5 is also rational This contradicts the fact that√5 is irrational number. This assumption is wrong so 7√5 is irrational.