Question

prove that root 11 is an irrational number and hence show that 2-root 11 is irrational number

Answer 1

Answer:

Hello mate..

Step-by-step explanation:

Let as assume that √11 is a rational number.

A rational number can be written in the form of p/q where q ≠ 0 and p , q are non negative number.

√11 = p/q ....( Where p and q are co prime number )

Squaring both side !

11 = p²/q²

11 q² = p² ......( i )

p² is divisible by 11

p will also divisible by 11

Let p = 11 m ( Where m is any positive integer )

Squaring both side

p² = 121m²

Putting in ( i )

11 q² = 121m²

q² = 11 m²

q² is divisible by 11

q will also divisible by 11

Since p and q both are divisible by same number 11

So, they are not co - prime .

Hence Our assumption is Wrong √11 is an irrational number .

HOPE IT WILL HELP YOU ❣️❣️❣️....

PLZ MARK AS BRAINLIST ANSWER ❣️...

PLZ FOLLOW ME ✔️✔️

Answer 2

Answer:

Let us assume 2√11 is rational.

therefore, it can be written as p/q, where q=/=0

so, 2√11 = p/q

(taking 2 on other side), √11 = p/2q

LHS is irrational, and RHS is rational. This contradiction has occured due to our incorrect assumption that 2√11 is rational.

therefore, 2√11 is irrational.

hope this helps you