1.

Prove that 3√7 is irrational number​

Answer»

Answer:

But root 7 is an irrrational number and -p+3q/q is a rational no. This means irrational no. is EQUAL to rational no.

Step-by-step explanation:

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.


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