Question

Show that 6+√2 is a rational number​

Answer 1

Answer:

Let us assume 6+

2

is rational. Then it can be expressed in the form

q

p

, where p and q are co-prime

Then, 6+

2

=

q

p

2

=

q

p

−6

2

=

q

p−6q

-----(p,q,−6 are integers)

q

p−6q

is rational

But,

2

is irrational.

This contradiction is due to our incorrect assumption that 6+

2

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is rational

Hence, 6+

2

is irrational

Answer 2

Answer:

IT MUST BE IRRATIONAL

Step-by-step explanation:

Let us assume 6+ √2 is rational. Then it can be expressed in the form p÷q , where p and q are co-prime

Then, 6+√2 = p÷q

√2 = p÷q −6

√2 = p−6q÷q -----(p,q,−6 are integers)

p−6q÷q is rational

But,

√2 is irrational.

This contradiction is due to our incorrect assumption that 6+√2 is rational

Hence, 6+√2 is irrational

NOT RATIONAL

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