Question

prove that 5+√3 is an irrational number​

Answer 1

Answer:

hope you know the proof of √3 being irrational

Step-by-step explanation:

let us assume on the contrary 5+√3 to be rational.

by defination of rational numbers you can write it as

5+√3=p/q where p and q are integers and q is not equal to zero HCF of p,q=1

transfer 5 on RHS

you get

√3= p-5q/q , which is rational

but this contradicts the fact that √3 is irrational

hence our assumption was wrong .

QED

Answer 2

Answer:

Well, √3 is an irrational number ( as it is a root of a non-square number)

•°• 5+√3 is still an irrational number as the sum of a rational and an irrational number is always an irrational number.

Proof of this

Let x be a rational number and y be an irrational number.

We have to prove that x+ y is an irrational number.

On the contrary, let us assume that x+y is a rational number.

We know that the difference of two rational numbers is always a rational number.

==>( x+y) - x is a rational number.

==> y is a rational number.

But y was an irrational number ( given)

•°• This is a contradiction.

==> x+ y is an irrational number.

Hence Proved

#answerwithquality

#BAL

PLEASE MARK MY ANSWER AS THE BRAINLIEST PLSSS