Question

Example 10 : Show that 5 - 13 is irrational.​

Answer 1

Answer:

let 5-root3 be rational

5-root 3 =p/q

root3= p/q -5 let this eqn be (i)

p/q -5 is rational

but root3 is irrational

From (i) we get that irrational number

=rational number,which is a contradict

therefore 5 - root 3 is irrational

Hope it is helpful✌️

Answer 2

5 - √3 is irrational

________ [TO SHOW]

Solution:

• Let us assume that √3 is rational number.

=> 5 - √3 = $\dfrac{a}{b}$

Here a and b are co-prime numbers

=> 5 - √3 = $\dfrac{a}{b}$

=> - √3 = $\dfrac{a}{b}$ - 5

=> - √3 = $\dfrac{a\:-5b}{b}$

=> √3 = $\dfrac{-a\:+\:5b}{b}$

=> √3 = $\dfrac{5b\:-\:a}{b}$

Here

$\dfrac{5b\:-\:a}{b}$ is rational number.

So, √3 is also a rational number.

But we know that √3 is irrational number.

So, our assumption is wrong.

5 - √3 is irrational number.

________ [HENCE PROVED]