Question

prove that root 3 is irrational

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Answer 1

Hello Mate,

Given: 3

To find: 3 is an irrational number.

Solution: v3=(Were p and q is a co-prime)

3xq Squaring both the side in above equation

{lsqrt {3 \times {a}{2}} = p2}

3 xf =P

if 3 is a factor of p?

Then, 3 will also be a factor of p

Let p-3 x m {where m is a integer)

Squaring both sides we get÷3xm =9xm

Substitute the value of p in the equation

3 x = 3 xq = 9 x m* =3 x m

If 3 is a factor of q

Then, 3 will also be factor of q

Hence, 3 is a factor of p & q both

So, our assumption that p & q are co

prime is wrong.

So, V3 is an "irrational number". Hence

proved.

Hope this helps you

Answer 2

Answer:

this is the solution

Step-by-step explanation:

let

$\sqrt{3}$

be a rational number

therefore,

$\sqrt{3}$

= p/q

squaring both side

$\sqrt{3} ^{2}$

= (p/q)2

q2=p2/3

if 3 divides p2 then 3 also divides p

therefore 3 is a factor of p other than 1

so it contracting our assumption that

$\sqrt{3}$

is rational number

therefore

$\sqrt{3}$

is ana irrational number.