Question

if root 3 is irrational, prove that 5-3 root 3 is irrational.
pls answer

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Answer 1

Answer: I hope this helps.  The answer is down below

Step-by-step explanation:

Let us assume that 5 - √3 is a rational   We can find co prime a & b ( b≠ 0 )such that  5 - √3  = a/b. Therefore 5 - a/b = √3. So we get 5b -a/b = √3 Since a & b are integers, we get 5b -a/b  is rational, and  so √3 is rational. But √3 is an irrational number. Let us assume that 5 - √3 is a rational. We can find co prime a & b ( b≠ 0 )such that  ∴ 5 - √3 = √3 = a/b. Therefore 5 - a/b = √3. So we get 5b -a/b = √3. Since a & b are integers, we get 5b -a/b  is rational, and so √3 is rational. But √3 is an irrational number Which contradicts our statement  ∴ 5 - √3 is irrational

Answer 2

Step-by-step explanation:

above explanation is your answer.

the 1st one is answer for , if it is about (5-root3)

And the second one may be the answer for, if it is about (5-3root3)