Question

prove that 5-√3 is irrational number​

Answer 1

Answer:

suppose 5-root3 is rational

5-root3=a/b

5=a/b -root3

by contradiction 5-root3 is irrational

Answer 2

Answer:

let root 3 is rational no.

Step-by-step explanation:

root3=a/b (a and b are co prime no.)

now,squaring on both sides.

we have,

(root 3)^2 =( a/b)^2

3=a^2/b^2

3b^2=a^2...(i)

b^2=a^2/3

since a^2 is divisible by 3

therefore a is also divisible by 3

a=3c

put a=3c in eq.(i)

3b^2=(3c)^2

3b^2=9c^2

3b^2/9=c^2

b^2/3=c^2

since b^2 is divisible by 3

therefore b is also divisible by 3

3 is a common factor which is contradiction.

hence root 3 is an irrational root.

now we have root 3 is irrational .

therefore 5-root 3 is also irrational no.