Question

Prove that 7+3 2root is not a rational number

Answer 1

answer

let 7 + 3√2 be an rational number where

7+3√2 = a/b [ a and b are coprime and b is not equal to zero]

3√2= a/b-7

3√2 =( a-7b) /b

√2 = (a-7b) /3b .....(i)

Now ,from equation (i) ,we get that √2 is rational but we know that √2 is irrational. so actually 7 + 3√2 is irrational not rational. thus our assumption is wrong. The number is irrational.

hope it help u

Answer 2

# Heya Mate #

Here is your answer

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To Prove :-

7+ 3√2 is irrational or not rational number.

Proof :-

Let 7+3√2 be a rational number

So, 7+3√2 = a/b

(where b≠0,a and b are Co prime

numbers)

Then, 3√2 = a/b - 7

By LCM

3√2= a - 7b/ b

√2 = a - 7 b / 3b

» Hence our supposition was wrong that 7+ 3√2 is rational because

√2 is a rational number and which can't be equal to a - 7b /3b which is a rational.

So, 7+ 3√2 is a irrational number

(not rational)

» You can also see in the attached image.

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» Hope it helped

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