Question

Prove Root 2 ia an irrational number

Answer 1

Proof:Let √ 2 is an rational number.

So, √2 = p/q (where p and q are co-prime number and q is not equal to 0)

Squaring Both Sides-

2 = p^2 / q^2

Cross Multiplying-

q^2 = 2 p^2 ………………………………………(1)

So, We can say that q^2 is divisible by 2 and q is also divisible by 2.

Let q = 2 r

Squaring Both Sides-

q^2 = 4 r^2 ………………………………………(2)

From Eq. 1 and 2-

2 p^2 = 4 r^2

Dividing Both Sides By 2-

p^2 = 2 r^2

So, We can say that p^2 is divisible by 2 and p is also divisible by 2.

From This we have reach a conclusion that p and q both divisible by 2.

It contradict the fact that p and q are co-prime numbers.

So, Our Supposition is wrong.

Hence, we can say that √2 is an irrational number.

Answer 2

Hey mate here is your answer ⤵⤵⤵⤵

$<b>Prove that √2 is an irrational number? Let √ 2 is an rational number. So, √2 = p/q (where p and q are co-prime number and q is not equal to 0) Squaring Both Sides- 2 = p^2 / q^2 Cross Multiplying- q^2 = 2 p^2 ………………………………………(1) So, We can say that q^2 is divisible by 2 and q is also divisible by 2. Let q = 2 r Squaring Both Sides- q^2 = 4 r^2 ………………………………………(2) From Eq. 1 and 2- 2 p^2 = 4 r^2 Dividing Both Sides By 2- p^2 = 2 r^2 So, We can say that p^2 is divisible by 2 and p is also divisible by 2. From This we have reach a conclusion that p and q both divisible by 2. It contradict the fact that p and q are co-prime numbers. So, Our Supposition is wrong. Hence, we can say that √2 is an irrational number.$

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