Question

Prove that 5+√2 is irrational given that √2 is irrational

Answer 1

Answer:

we know that √2 = 1.414... or non terminating and non repeating.

5+√2

=5+ 1.414...

6.414... which is also non terminating non repeating

hence 5+√2 is irrational

Hope it will help

Answer 2

GIVEN = √2 IS AN IRRATIONAL NO.

LET US SUPPOSE THAT THE 5+√2 IS AN RATIONAL NO.

HENCE,

5+√2=P/Q

√2=P/Q-5

√2=P/Q-5

HENCE √2 IS A. RATIONAL NUMBER

BECAUSE IT IS EQUAL TO THE P/Q FORM

BUT WE KNOW THAT √2 IS AN IRRATIONAL NO.  

HENCE, OUR ASSUMPTION IS WRONG

HENCE 5+√2 IS AN IRRATIONAL NUMBER

Hence, Proved

Thanks