Question

Prove that 4 - 5√2 is irrational

Answer 1

Answer:

Since x is a rational number, x2 is also a rational number.

⇒ 66 - x 2 is a rational number

⇒ (66−  x2 )/40 is a rational number  

⇒√2 is a rational number

But √2 is an irrational number, which is a contradiction.

Hence, our assumption is wrong.

Thus, (4 - 5√2) is an irrational number.

Answer 2

HEY MATE!!

let assume 4-5root2 is an rational number

4-5root2 = a/b

where a and b(b is not equal to 0) is a co-prime number

therefore HCF=1

4-5root2= a/b

-5root2= a/b-4

-5root2=a-4b/b

root2=a-4b/5b

root2 is an rational number

(since a and b are integers so, a-4b/5b is an rational number)

It contradits that root2 is an irrational number

so our assumption is wrong

HENCE 4- 5ROOT2 IS AN IRRATIONAL NUMBER

NO, 4-5 root 2 is an irrational number If the sum of 2 irrational number alway irrational number

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