Question

prove that 5-√3 is an irrational number..
step by step explanation...
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Answer 1

Answer:

let 5-✓3 is rational

5-√3=p/q where p and q are integers and q is not equal to 0

√3=p+5/q

here √3 is irrational and p+5/q is rational which is never possible

and our supposition is wrong

hence,5-√3 is irrational proved

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Answer 2

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.