Question

prove that✓3 is irrestional number​

Answer 1

Answer:

√3 can be written in the form a/b

where a and b (is not equal to 9)

√3=a/b

√3b=a square both side

(√3b^2)=a^2

3b^2=a^2

a^2/3= b^2

3 shall also divide a. equation 1

a/3=c where c is some integer

a=3c

We know that

3b^2=a^2

putting a =3c

3b^2=(3c^2)

3b^2=9 c^2

b^2=1/3*9c^2

b^2=3c^2

b^2=c^2

Hence 3 divide b square

3 divide b also equation 2

By 1 and 2

3 divide both a and b

hence 3 is factor of a and b

so,a and b have a factor 3

a and b are not Co prime

√3 is irrational

Hope it helps u!!!

Answer 2

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Answer:

√3 can be written in the form a/b

where a and b (is not equal to 9)

√3=a/b

√3b=a square both side

(√3b^2)=a^2

3b^2=a^2

a^2/3= b^2

3 shall also divide a. equation 1

a/3=c where c is some integer

a=3c

We know that

3b^2=a^2

putting a =3c

3b^2=(3c^2)

3b^2=9 c^2

b^2=1/3*9c^2

b^2=3c^2

b^2=c^2

Hence 3 divide b square

3 divide b also equation 2

By 1 and 2

3 divide both a and b

hence 3 is factor of a and b

so,a and b have a factor 3

a and b are not Co prime

√3 is irrational

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