Question

given that under root 2 is irrational number prove that (5+3under root 2 is an irrational nber

Answer 1

Hey.. I think this can be ur answer dear!!

Given :root 2 is irrational..

Now, let us assume that 5+3 root 2 is rational
So,
5+3root2 =a/b
3root2 =a/b-5 = a-5b/b
root2=a-5b/3b

BUT we know that root 2 is irrational
Hence our assumption was wrong
5+3root2 is irrational.

Hence proved
Hope it helps you dear ☺️☺️☺️

Answer 2

Hi...Here's your answer.

Step-by-step explanation:

Given, under root 2 is irrational.

Let,  5+(3*under root 2) be a rational number r

5+ (3*under root 2)=r (r not equal to 0)

or, 3*under root 2=r-5

or, under root 2=(r-5)/3

Since, r is a rational number and r is not equal to 0

Therefore, (r-5)/3 is rational

or, under root 2 is rational

However, this contradicts that under root 2 is irrational

Therefore, our statement is false and r is irrational

Or, 5+(3* under root 2) is irrational (hence proved).