Question

prove that root 3 + 5 is irrationalnumber​

Answer 1

HEY!

REFER TO THE ATTACHMENT ABOVE ❤

HOPE IT HELPS UHH ❤

Answer 2

Step-by-step explanation:

let root 3 is rational

if root 3 is rational then it must be equal to p/q where p and q are coprime and q is not equal to zero

root3=p/q

squaring both sides

3=p square/q square

3q square= p square ...............1

3 is a factor of p square

3 is a factor of p

now,

let p= 3r

squaring both sides

p square= 9r square

from 1,

3q square= 9r square

q square = 3r square. ............2

3 is a factor of q square

3 is a factor of q

From 1 and 2 we get,

3 is factor of p and q both which is a contradiction to our supposition because p and q were coprime

Hence,

root3 is irrational

and also root 3 +5 is irrational because

now it doesnot matter that now root 5 is rational or irrational as

rational +rational=rational

irrational +rational= irrational

therefore,

root3 +5 is irrational