Question

how to classify √7 is rational or irrational number ​

Answer 1

Answer:

A rational number is defined as a number that can be expressed in the form of a quotient or division of two integers, i.e. p/q, where q is not equal to 0.

IN DETAIL:-

A rational number is defined as a number that can be expressed in the form of a quotient or division of two integers, i.e. p/q, where q is not equal to 0. √7 = 2.645751311064591. Due to its never-ending nature after the decimal point, √7 is irrational.

HENCE √7 IS IRRATIONAL

Please mark me brainliest

Answer 2

Answer:

root7 is an irrational number.

Step-by-step explanation:

lets assume that root 7 is rational

so root7=a/b (rational numbers can be written in p/q form)

and hcf(a,b)=1

now,

a=root7b

on squaring both sides

a²=root7²b²

a²=7b²

so 7 is a factor of a²

and thus 7 is also a factor of a

now

a=7k (where k is any number)

similarly

a²=root7b

(7k²)=root7b²

49k²=7b²

7k²=b²

thus 7 is factor of b²

and also 7 is factor of b

now as we know

hcf(a,b) = 7

but it should be 1 as we assumed, and hence our assumption is wrong.

thus root 7 is an irrational number

holy cheese i just typed this answer for literally no reason :/ i really hope this helped