Question

Examine whether the following numbers are rational or irrational2√3/3√52-4√117

Answer 1

Answer:

Step-by-step explanation:

A rational number is defined as a number which can be expressed as a fraction , where and fraction in its lowest terms. ... X is an irrational number if it cannot be written as the ratio of two different integers. 2 can be written as 2/1, as there is a 1 under every integers. So 2 is not an irrational number.

2 is an rational number.

Let us assume 3-√3 is rational

let 3-√3 = a/b (a,b are any integers)

=> 3 - a/b = √3

=> √3 = 3 - a/b

=> √3 = 3b-a/b

For any two integers, RHS (3b-a/b) is rational

But, LHS(√3) is irrational

A rational and irrational are never equal

So, our assumption is false

Therefore, 3-√3 is irrational number.

   

root 52 -4 is irrational number because root 52 is not an perfect square  so, if we subtract 4 from root 52 we will get answer in decimal.

we will get (2 * root 13 -4)

root 117 is an irrational number as root 117 is not an perfect square.

root 117 = 10.81