Question

show that 5-2 root 3 is an irrational number​

Answer 1

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Let us assume that 5-2√3 is rational

5-2√3 = p/q ( where p and q are co prime)

-2√3 = p/q-5

-2√3 = p-5q/q

-√3 = p-5q/2q

√3 = 5q-p/2q

now p , 5 , 2 and q are integers

∴ 5q-p/2q is rational

∴ √3 is rational

but we know that √3 is irrational . This is a contradiction which has arisen due to our wrong assumption.

∴ 5-2√3 is irrational

Answer 2

Step-by-step explanation:

Let us assume that 5-2√3 is rational

5-2√3 = p/q ( where p and q are co prime)

-2√3 = p/q-5

-2√3 = p-5q/q

-√3 = p-5q/2q

√3 = 5q-p/2q

now p , 5 , 2 and q are integers

∴ 5q-p/2q is rational

∴ √3 is rational

but we know that √3 is irrational . This is a contradiction which has arisen due to our wrong assumption.

∴ 5-2√3 is irrational