Question

prove that
$\sqrt{2 - \sqrt{3} }$
prove that
irrational number ​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Proof-

Let us assume that √2-√3 is a rational number

Therefore

√2-√3 = a/b. (a and b are co-prime and b is not equal to zero and there's comman factor is 1)

=. a=b√2-√3

Squaring on both sides

a²= (2-√3)b²----------------1

= (2-√3) divides a² completely

=(2-√3) divides a completely

Where,

a/(2-√3) =c. (C is quotient)

Cross multiplying

a=(2-√3) c

Squaring on both sides

a²=7-4√3---------------2

Form 1 and 2

(2-√3)b²=7-4√3

7-4√3/(2-√3) is the factors of b²

7-4√3/(2-√3) divides b

Form this we can say that our assumption is worng because a and b have more than 1 comman factors

Hence it is not rational

Step-by-step explanation: