Question

if √ab is rational prove that √a+√b is irrational

Answer 1

Let us suppose that √a + √b is a rational number.

So, we can write √a + √b as

√a + √b = p/q .........1 where q ≠ 0

Now, squaring on both side, we get

      (√a + √b)2 = (p/q)2

=> a + b + 2*√a * √b = p2 /q2

=> a + b + 2*√(ab) = p2 /q2

=> 2*√(ab) = p2 /q2 - (a + b)  ............2

Since, √a + √b are rational, So a and b are also rational.

So, RHS of equation 2 is a rational number.

But it is given that √(ab) is an irrational number.

So, LHS of equation 2 is an irrational number.

which contradict our assumption.

Answer 2

Step-by-step explanation:

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