Question

prove that root 5 is irrational number short form​

Answer 1

HEYA MATE HERE IS YOUR ANSWER...

LET AS PER OUR CONTRADICTION √5 IS RATIONAL, WHERE P&Q ARE CO PRIME NUMBERS. SO,

» √5 = p/q

TRANSFERRING Q ON L.H.S....

» √5q = p

SQUARING BOTH SIDES....

» (√5q)² = p²

» 5q² = p² ---------<1>

NOW, TAKING AGAIN SQUARE...

» (5q)² = p²

» 25q² = p² ------------<2>

NOW, PUTTING THE VALUE OF P FROM EQ (1) TO (2) ....

SO, 25 q² = 5 p²

» 5q² = p²

THEREFORE, √5 IS RATIONAL.

BUT, OUR CONTRADICTION PROVES WRONG.

»»√5 IS IRRATIONAL.

HOPE THIS HELPS....
PLZ MARK ME AS BRAINLIST..

Answer 2

let us assume that √5 is a rational number in the form of p/q where p a and are co-prime positive integers and q is not equal to 0.

so,

√5=p/q

(squaring both sides)

5=p2/q2

p2= 5q2. (1)

5 is a factor of p2

5 is the factor of p also.

So, let p=5m for some integer m

From(1),we get

5q2= 25m2

q2=5m2

5 is the factor of q2

5 is the factor of q also.

This contradicts our assumption that p and q are co prime.

Therefore √5 is an irrational number.

Mark it the brainliest