Question

Prove that √3 ber.
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Answer 1

Answer:

If possible , let

3

be a rational number and its simplest form be

b

a

then, a and b are integers having no common factor

other than 1 and b



=0.

Now,

3

⟹3=

b. a

2 2

(On squaring both sides )

or, 3b 2 =a 2 .......(i)⟹3 divides a 2

(∵3 divides 3b 2 )⟹3 divides a

Let a=3c for some integer c

Putting a=3c in (i), we get

or, 3b 2 =9c2 ⟹b 2 =3c 2⟹3 divides b 2

(∵3 divides 3c 2 )⟹3 divides a

Explanation:

Hope it's helpful to you

but don't know it is right answer or no..

Answer 2

Answer:

If possible , let

3

be a rational number and its simplest form be

b

a

then, a and b are integers having no common factor

other than 1 and b



=0.

Now,

3

⟹3=

b. a

2 2

(On squaring both sides )

or, 3b 2 =a 2 .......(i)⟹3 divides a 2

(∵3 divides 3b 2 )⟹3 divides a

Let a=3c for some integer c

Putting a=3c in (i), we get

or, 3b 2 =9c2 ⟹b 2 =3c 2⟹3 divides b 2

(∵3 divides 3c 2 )⟹3 divides a

Explanation:

Hope it's helpful to you

but don't know it is right answer or no..