Question

prove that root 5 is irrational
fast give me answer​

Answer 1

Step-by-step explanation:

let root 5 is rational

then√5=p/q

p=q√5

squaring on both sides

p^2=q^2*5

q^2=p^2/5

so 5 divides p square and also p

let p=5m

now 5^2*m^2/5=q^2

now msquare=q square by5

5divides q square and also q

so 5 is prime

but this contradicts √5 is irrational

so √5is irrational

Answer 2

Answer:

Let ✓5 be a rational number.

Then it can be written as √5=a/b

✓5b=a

now, squaring both sides

(✓5b)²=a²

5b²=a²

a² is divisible by 5.

a is also divisible by 5.

now,

5b²=(5m)² (let m be any integer)

5b²=25m²

b²=5m

b² is divisible by 5

b is also divisible by 5.

hence,

a and b have common factor 5 other than 1.

this contradiction has arisen because of our wrong assumption.

Therefore, ✓5 is irrational.