Question

show that 8-2 root 5 is Ir-rational

Answer 1

Answer:

Let 8-2√5 be a rational number

Say, 8-2√5= r where r is a rational number

⇒8-r= 2√5

⇒√5= $\frac{8-r}{2}$

Since r is a rational number, therefore $\frac{8-r}{2}$ is also a rational number.

⇒ √5 is a rational number

But we know that √5 is irrational.

Therefore our assumption that 8-2√5 is rational number is wrong.

Therefore, 8-2√5 is irrational.

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