Question

prove this number is irrational
$\sqrt{7}$
with explaintion​

Answer 1

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. so our assumption is wrong by this we can prove that root 7 is irrational.

$\huge \: thank \: you$

Answer 2

Answer:

Question

$= prove \: \sqrt{7} \: is \: a \: irrational \: number$

First find the solution of it :

$\sqrt{7}$

$= 2.64575131106............ \:$

EXPLANATION:

See , this number can't be expressed in the ratio . So , they are called irrational number .

And it is a number in which it's decimal places will go to forever. So , it is a irrational number .

HOPE IT HELPS YOU