Question

find the square root of 3 by division method hence show that √3 is an irrational number
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Answer 1

above is your answer

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Prove that sqaure root of 3 is an irrational number.

Answer:

Let us assume to the contrary that √3 is a rational number.

It can be expressed in the form of p/q

where p and q are co-primes and q≠ 0.

⇒ √3 = p/q

⇒ 3 = p2/q2 (Squaring on both the sides)

⇒ 3q2 = p2………………………………..(1)

It means that 3 divides p2 and also 3 divides p because each factor should appear two times for the square to exist.

So we have p = 3r

where r is some integer.

⇒ p2 = 9r2………………………………..(2)

from equation (1) and (2)

⇒ 3q2 = 9r2

⇒ q2 = 3r2

Where q2 is multiply of 3 and also q is multiple of 3.

Then p, q have a common factor of 3. This runs contrary to their being co-primes. Consequently, p / q is not a rational number. This demonstrates that √3 is an irrational number.

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Answer 2

Answer:

The first pic answer is for find the square root of 3 by division method: Here √3 is non terminating & non repeating. So they are irrational number.

2nd and 3rd pic is for show that√3 is an irrational number.