Question

Show that ³√7 is not a rational number.​

Answer 1

ANSWER

We have to prove that 3+

7

is irrational.

Let us assume the opposite, that 3+

7

is rational.

Hence 3+

7

can be written in the form

b

a

where a and b are co-prime and b



=0

Hence 3+

7

=

b

a

⇒

7

=

b

a

−3

⇒

7

=

b

a−3b

where

7

is irrational and

b

a−3b

is rational.

Since,rational



= irrational.

This is a contradiction.

∴ Our assumption is incorrect.

Hence 3+

7

is irrational.

Hence proved.

Answer 2

Answer:

ok............................