\huge \blue{ \bold {  \pmb{ \fcolorbox{gray}{black} {  {\ \ddag  \: \ \red{QUESTION}\  \ddag  \:  }}}  }}

Question

\huge \blue{ \bold {  \pmb{ \fcolorbox{gray}{black} {  {\ \ddag  \: \ \red{QUESTION}\  \ddag  \:  }}}  }}

Prove that √7 is an irrational number.​

in progress 0
Iris 11 months 2021-07-07T15:06:55+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-07-07T15:08:37+00:00

    Explanation:

    as our assumsion p & q are co prime but it has a common factor. So that √7 is an irrational.

    0
    2021-07-07T15:08:44+00:00

    Lets assume that √7 is rational number. ie √7=p/q.

    suppose p/q have common factor then

    we divide by the common factor to get √7 = a/b were a and b are co-prime number.

    that is a and b have no common factor.

    √7 =a/b co- prime number

    √7= a/b

    a=√7b

    squaring

    a²=7b² ..1

    a² is divisible by 7

    a=7c

    substituting values in 1

    (7c)²=7b²

    49c²=7b²

    7c²=b²

    b²=7c²

    b² is divisible by 7

    that is a and b have atleast one common factor 7. This is contridite to the fact that a and b have no common factor.This is happen because of our wrong assumption.

    √7 is irrational

Leave an answer

Browse

9:3-3+1x3-4:2 = ? ( )