Question

Q5. Prove that 11 - 7 root 2 is an irrational number.​

Answer 1

Step-by-step explanation:

Let's assume, on the contrary, that 11 - 7√2 is a rational number,

We know that,

A number is said to be rational when, it can be represented in the p/q form, where p and q are integers and they are coprimes and q is not equal to 0.

then,

p/q = 11 - 7√2

7√2 = 11 - p/q

7√2 = (11q - p)/q

√2 = (11q - p)/7q

Now, we know that, p and q are integers, thus, 11q, p, and 7q are integers and so, are rational numbers, but √2 is an irrational number.

And, we know that, an irrational number can't be equal to a rational number.

Thus, this contraction has risen due to our incorrect assumption statement.

Hence, 11 - 7√2 is an irrational number.

Hope it helped and believing you understood it........All the best

Answer 2

Step-by-step explanation:

get ft try FDTD hjiuiyughuth ujrj fbfnbfbf f d d f d f f f f f f