Question

given that root 2 is irrational prove that 5 + 3 root 2 is an irrational number​

Answer 1

as we are given that √2 is irrational .

to prove : 5 + 3√2 = irrarational

let 5 + 3 √2 = a / b where a and b both are integers and b is not = to 0

5 + 3 √2 = a / b

3√2 = a / b - 5

3√2 = a - 5b / b

√2 = a - 5b / 3b

now , we know a , b , 5 and 3 all are integers

√2 = integers

all integers are also rational numbers.

√2 = rational no.

which is wrong as we are given that √2 is irrational . so 5 + 3 √2 is also an irrational no.

also ,

rational no. + irrational no. = irrational no.

regards !! mark me brainliest dear❤❤

Answer 2

Hii Arpita, refer to the attachment for ur answer