Question

prove sqrt 7 is irrational with explainnation​

Answer 1

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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

Answer 2

Step-by-step explanation:

It is known that a decimal number that has a value that does not terminate and does not repeat as well, then it is an irrational number. The value of √7 is 2.64575131106... It is clear that the value of root 7 is also non-terminating and non-repeating. This satisfies the condition of √7 being an irrational number.