Question

prove √7 is irrational​

Answer 1

hi mate

solution

√7 why irrational...

so..mate here you know that √7=a/b ( here a and b are co prime means they have only 1 as common factor. ... then mate

Here we find 7 is common which divide both a and b but this is contradiction because a and b are co prime they don't have common factor other than 1.

So for our assumption is wrong. Hence √7 is irrational.

so explaination here 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

i hope it helpfull to you

Answer 2

hey mate ur ans is in the attachment

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