Question

Prove that root 5 is irrational.​

Answer 1

because root 5 is neither terminating nor repeaing

Answer 2

Step-by-step explanation:

Let √5 as rational number.

So we can write it in the form of p/q.

where p and q are co primes and q ≠ 0.

Now squaring both sides.

√5 ^2 = ( p/ q)^2

5 = p^2/q^2

p^2 = 5q^2

p^2/5 = q^2

If p^2 is divisible by 5 .

Then p can also be divisible by 5.

So p is any multiple of 5

So let 5c = p

Now squaring both sides.

25c ^2 = p^2

putting value of p^2.

25 c^2 = 5 q^2

5 c^2 = q^2

c ^2 = q^2/5.

If q^2 is divisible by 5 then q is also divisible by 5 .

So q is also a multiple of 5.

P and Q have a common factor 5 other than 1 . So these are not co prime.

Our hypothesis was wrong

√5 is irrational number.

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Hope it may help you.♥♥♥