Math, asked by ishaa1180, 1 year ago

If √ab is an irrational number,prove that √a+√b is rational​

Answers

Answered by Siddhantsinghthakur
3

Answer:

let ✓a +✓b be a rational no.

equals to p/q where qis not equal to zero

✓a + ✓b = p/q

squaring on both the side

(✓a+✓b)² = (p/q)²

using the identity (a+b)² = a²+b²+2ab

(✓a)² +(✓b)²+2✓a✓b = (p/q)²

a+b+2✓ab =(p/q)² [hence ✓a✓b = ✓ab]

shifting ...

2✓ab = (p/q)² - (a+b)

✓ab = { (p/q)² - (a+b) } /2

hence rational no. is not equal to irrational no.

as because ✓ab is an irrational no. which is given

hense it's a irrational no..

then ✓a +✓b is not a rational no

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