Question

prove that 8-√6 is irrational​

Answer 1

Let 8-√6 is a rational number then we get that a and b two co-prime integers.

Such that 8-√6 =a/b where b not equal to zero

root 6 = 8-a/b Since a and b are two integers.

Therefore (8-a/b)is a rational number and

So root 6 also is a rational number.

But it is contradiction to fact root √6 is irrational number.

So we conclude that 8- √6 is an irrational number.

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Answer 2

Answer:

8-√6 is an irrational number..

Step-by-step explanation:

If possible, let 8-√6 is a rational number.

then, it is written as , 8-√6 = p/q form

:- where p and q are

co-prime number.

= 8-√6 = p/q

= 8 = p/q +√6

= 8 = p + √6q /q

= 8q = p +√6q

= 8q-p /q = √6

√6 is rational.. { q and p are integer ,

:- 8q-p / q is a rational }

= This contradict the fact that √6 is irrational.

= So, our supporting is incorrect.

= Hence, 8-√6 is an irrational number