Question

Prove that 15 + 17√4 is an irrational number..!!​

Answer 1

Answer:

Step-by-step explanation:

let us assume 15+17$\sqrt{4$ to be rational number and given that $\sqrt{4$ is irrational

then ,

15+17$\sqrt{4$ =p/q ..................where p and q are coprime and q is not equal to zero

so,

17$\sqrt{4$ =(p/q ) -15

17$\sqrt{4$ = (p -15)/q

$\sqrt{4$ = (p-15)/17 q

as rhs of the equation is rational that means $\sqrt{4$ is also rational .

but this contradicts our fact that $\sqrt{4$ is irrational .

thus 15+17$\sqrt{4$ is irrational.

hence,proved

Answer 2

Answer:

Let 15+17√2 is a rational number

we know that any rational no. it is in the form of p/q ,where pand q are co-prime no.

15+17√2=p/q

17√2=p/q -15

√2=p-15q/17q ...........(I)

here, p and q are some integers

therefore, p-15q/17q is a rational no.

but, √2 is irrational no.

it contradicts our supposition

=> 15+17√2 is irrational .............(hence proved)

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