Math, asked by pratapsachin12p7haba, 1 year ago

prove that 3-2√5 is irrational

Answers

Answered by nicky51

3-2=1
so , then your answer will be 1 underroot5
five does not have its own perfect square so it is irrartional.
hope it helps u
.......love u alll.....,

Answered by philheath

let us assume the fact that 3-2root5 is rational no.

$3 -2 \sqrt{5} = p \div q$
where p and q are integers and co prime
squaring on both sides

$9 + 20 - 12 \sqrt{5}$
= 29 - 12 root 5

philheath: 29 -

philheath: root 5 = p/q

philheath: 29-p/q=root 5

philheath: as p and q are integers therefore 29-p/q is rational no.

philheath: so, root 5 is also rational no. but this contradicts the fact that root 5 is irrational no.

philheath: this contradiction arises due to our wrong assumption

philheath: therefore it is irrational no.

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