Question

Prove that √3 or √5 is irrational.

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Answer 1

Step-by-step explanation:

A rational number can be written in the form of p/q where p,q are integers. p,q are integers then (p²+2q²)/2pq is a rational number. Then √5 is also a rational number. ... Therefore, √3+√5 is an irrational number.

I hope that will be help you my friend

Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{QuestioN :}}}}$

Prove that √3 or √5 is irrational.

GiveN :

• √3 + √5

To Prove :

• Prove that irrational.

$\huge \boxed{ \underline{ \underline{ \bf{SolutioN :}}}}$

Letus assume that 3 + √5 is a rational number.

So it can be written in the form a/b

3 + √5 = a/b

Here a and b are coprime numbers and b ≠ 0

By Solving,

3 + √5 = a/b

we get,

=>√5 = a/b – 3

=>√5 = (a-3b)/b

=>√5 = (a-3b)/b

This shows (a-3b)/b is a rational number.

But we know that √5 is an irrational number, it is contradictsour to our assumption.

Our assumption 3 + √5 is a rational number is incorrect.

3 + √5 is an irrational number

∴Hence, proved!