Question

classify the following number as rational or irtational. 5_√3​

Answer 1

Answer: irrational

Step-by-step explanation:

Answer 2

Step-by-step explanation:

let 5√3 be in p/q form where p and q be any coprime

p and q be any coprime5√3 =p/q

p and q be any coprime5√3 =p/q√3=p/5q

let √3 be in the p/q form and p and q are other coprime

√3 =p/q

√3q =p

square on both sides

3q^2 =p^2 ...(1)

q^2 = p^2/3

3divides p^2

3divides p

let p =3k where k is positive integer

3q^2 =3k^2

3q^2 =9k^2

q^2 =3k ^2

k^2 = q^2/3

3 divides q^2

3divides q

p and q are divisible by 3our assumption that p and q are coprime is wrong hence √3 is not rational but it is irrational

we know that √3 is irrational number

we know that √3 is irrational number therefore 5√3 is irrational