Question

if √2 is irrational prove that 3+5√2 is irrational​

Answer 1

Answer:

Step-by-step explanation:

Given √2 is irrational.

Let us assume that 3+5√2 is not an irrational number. Then it is a Rational Number.

So,3+5√2= p/q[ in its simplest form ]

Then,

3+5√2=a/b

5√2=a/b-3

5√2=a-3b/b

√2=a-3b/b×1/5

√2=a-3b/5b

√2=p/q [where a-3b=p and 5b=q]

We Know That,√2 is an Irrational Number.

So,our assumption is wrong.

Therefore,3+5√2 is an Irrational Number.

Hence Proved...

Hope This Helps You.

Please marks as Brainliest!!!

Answer 2

Given

√2 is irrational

To prove

3+5√2 is irrational

proof

WE KNOW THAT MULTIPLICATION OF A RATIONAL AND IRRATIONAL NUMBER IS ALWAYS IRRATIONAL

SO, 5 X √2 is irrational ... 1

NOW WE ALSO KNOW THAT

ADDITION OF A RATIONAL AND IRRATIONAL NUMBER IS ALWAYS IRRATIONAL

SO,

3+5√2 IS IRRATIONAL

HENCE THE PROOF

PLEASE MARK MY ANSWER AS BRAINLIEST ANSWER...........