Question

prove that root 7 is irrational ​

Answer 1

let root 7is a rational number were p and q are some integers q not =0

let a and b are the simplest form of p and q . these are Co-prime having only 1 factor.

√7=a/b

squaring on both sides

7=a sqo and b sqo

or

7b sq= a sq (i)

7 divide a sq

7 divide a also or theroeom 1.3

let a/7=c

then a=7c

squaring on both sides we get

a sq. 49c sq. (2)

c sq =49/a sq

a sq divide 49

put the a sq in

equation (1)

7b sq = 49 c sq

7 divide b sq

so, there a and b have at least 7 common factor other than 1.

This contradiction has arisen because of our incorrect assumption. √7 is a irrational.

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