Question

prove that 2+root3/5 is an irrational number given that root 3 is irrational number?? please fully explain this question​

Answer 1

Answer:

Let's assume that 2+root 3/5 is rational.

So, we can represent it as 2+root3/5 as a/b ( a and b are integers, b not equal to zero and a&b are coprime)

2+root3/5=a/b

root3/5=a/b-2

root3/5=a-2b÷b

root3=5(a-2b)÷b

Now as 5 (a-2b)÷b is rational so root3 is also rational.

However given that root3 is irrational.

But this contradicts our assumption.

This contradiction arises due to our wrong assumption that 2+root3/5 is rational.

Therefore 2+root3/5 is irrational.

Hence Proved

Hope this helps you!!

Answer 2

Answer:

Let's assume that 2+root 3/5 is rational.

So, we can represent it as 2+root3/5 as a/b ( a and b are integers, b not equal to zero and a&b are coprime)

2+root3/5=a/b

root3/5=a/b-2

root3/5=a-2b÷b

root3=5(a-2b)÷b

Now as 5 (a-2b)÷b is rational so root3 is also rational.

However given that root3 is irrational.

But this contradicts our assumption.

This contradiction arises due to our wrong assumption that 2+root3/5 is rational.

Therefore 2+root3/5 is irrational.

Hence Proved

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