Question

prove that ✓m+✓n is irrational, if ✓mn is irrational​

Answer 1

Answer:

HOPE IT HELPS YOU !!!

Step-by-step explanation:

TO PROVE :

root(m) + root(n) is irrational

GIVEN :

root(mn) is irrational

SOL:

[ root(m) + root(n) ] ^2 = [root(m)]^2 + [root(n)]^2 +2*root(m)*root(n) = m+n+2root(mn)

Here root(mn) is irrational.

If we multiply rational number to irrational number then the product is irrational, so 2root(mn) is irrational.

when we add something to irrational number the sum we get is always irrational.

so m+n+2root(mn) is irrational,

=> [root(m) + root(n)]^2 is irrational

Now the root of any irrational number is also irrational,

Therefore root(m) + root(n) is irrational.

Hence Proved.