Question

identify the rational number - 5-√3 , 5+√3 , 4+√2 , 5+√9 plz, answer with proper explanation.

Answer 1

Given

• 5-√3
• 5+√3
• 4+√2 ,
• 5+√9

√2 be irrational

These are the some terms

To find

We have to identify which is rational

Solution

1).

5-√3

Let 5-√3 be the rational no

Then

5-√3 =a/b

=>-√3 = a/b - 5

=>√3= 5b-a/b

Here 5b-a/bis a rational no then √3 be also rational

But in given √3 is irrational

Therefore our assumption is wrong.

Hence,5-√3 be a irrational

Irrational

2).

5+√3

5+√3=a/b

√3 =a/b-5

=>-√3 = a/b - 5

=>√3= -5b+a/b

Here -5b+a/bis a rational no then √3 be also rational

But in given √3 is irrational

Therefore our assumption is wrong.

Hence,5+√3 be a irrational

Irrational

Similarly

4+√2 , 5+√9 irrational

Hence ,given all terms are irrational