Question

show that 5+4√3 is irrational

rational number class 10th ​

Answer 1

Step-by-step explanation:

let us suppose 5+4√3 is rational number

5+4√3=a/b where a and b are integer

4√3=a/b-5

√3=a-5b/4b

right hand side is rational number

it implies √3 is rational number

but we know √3 is irrational number

hence our supposition is wrong

5+4√3 is irrational number

Answer 2

Answer:

Let us assume that 4−5  

3

​  

 be rational  

⟹4−5  

3

​  

=  

b

a

​  

 where a,bϵZ

⟹−5  

3

​  

=  

b

a

​  

−4

⟹  

3

​  

=  

5

4

​  

−  

b

a

​  

 

L.H.S = irrational number as  

3

​  

 is a irrational number.

R.H.S = rational number

as RHS



=LHS

Hence, our assumption is wrong and 4−5  

3

​  

 is a irrational number.