Question

ii) Show that 3+ V5 is irrational number.
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Answer 1

Step-by-step explanation:

Let √3 + √5 = a, where a is rational. As the right hand side is rational number while V5 is irrational. Since, 3 and 5 are prime numbers. Hence, √3 + √5 is irrational.

Answer 2

Let us ɑssume thɑt 3 + √5 is ɑ rɑtionɑl number.

Now,

3 + √5 = (p /q)

[Here p ɑnd q ɑre co-prime numbers]

√5 = [(p /q) - 3]

√5 = [(p - 3q) / q]

Here, {(p - 3q) /q} is ɑ rɑtionɑl number.

But we know thɑt √5 is ɑ irrɑtionɑl number.

So, {(p - 3q) /q} is ɑlso ɑ irrɑtionɑl number.

So, our ɑssumption is wrong.

3 + √5 is ɑ irrɑtionɑl number.

Hence, proved.

I hope this will help you dear..

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