Question

1) Prove that 3-2√5 is irrational?
2) Prove that 7-√2 is irrational?
3) Prove that 2+√7 is irrational?

Answer 1

➡️ 1) let 3-2√5 be a rational no.

so, 3-2√5 = a/b

√5 = a/2b - 3

a/2b-3 is a rational number

so, √5 also a rational no.

but, a qontradiction fact is that √5 is an irrerational no.

so, 3-2√5 is an IRRERATIONAL no. ❤️

similar you can do remaining 2 ❤️

ALL THE BEST FOR YOUR BOARDS ❤️✌️

Answer 2

Answer:

Let us assume ,

3+2√5 is rational.

So , 3+2√5 = a/b

a and b are coprimes

2√5 = a/b -3

√5 = a-3b /2b

Thus implies , √5 is rational which is incorrect . ( a and b are coprimes)

Thus our assumption that 3+2√5 is rational is incorrect.

So , 3+2√5 is irrational .

Hope it help you ✌️❣️