Question

prove that 6 + root 12 is an irrational number​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Let us assume that 6+√12 is rational.

That is , we can find coprimes a and b (b≠0) such that

6+root{12}=\frac{a}{b}6+

2

=

b

a

\implies root{12}=\frac{a}{b}-6⟹

2

=

b

a

−6

\implies root{2}=\frac{a-6b}{b}⟹

2

=

b

a−6b

Since , a and b are integers , \frac{a-6b}{b}

b

a−6b

is rational ,and so √12 is rational.

But this contradicts the fact that √12 is irrational.

So, we conclude that 6+√12 is irrational.

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