Question

prove that 5-√3 is irrational​

Answer 1

Answer:

if you have read the chapter one similar questions is there,

prove that √3 is irrational

from. that we can prove that 5-√3 is also an irrational no.

Answer 2

Answer:

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Let us assume that 5-√3 is rational number so we can find two integers a , b. Where a and b are two co - primes number.

= 5-√3 = a/b

= √3= 5- a/b

=> a and b are integers so (5 - a/b ) is rational

But √3 is irrational ( we know that and it is given)

So it arise contradiction due to our wrong assumption that 5 - √3 is rational number.

Hence, 5 -√3 is irrational number.