Question

04. Show that V7 is irrational,​

Answer 1

Answer:

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

Explanation:

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Answer 2

Answer:

hopes are all urs

Explanation:

let us assume ,to the contatry that √7 is rational .

so we can find the co prime integer a and b were ( b is not equal to 0 ) , such that ;

==> √7 = a/b

==> √7b = a

squaring on both sides , we get

2 2

7b = a

2

7 divides a.

7 divides a . ( therom 1.3)

so , we can write

a = 7 c for some integer c .

substituting for a , we get ;

7 b2 = ( 7c) 2

7 b2 = 49 c2

b2 = 7 c2.

this means ;. 7 divides c2

7 divides c .

==> a and b have at least 7 as a common factor.

===> But this contradicts the fact that a and b have no common factor other than 1.

=====> This contradiction arose due to are worng assumption that √7 is a rational number .

so we coclude that √7 is irrational ..