Question

Prove that root 5-root3 is a irrational number

Answer 1

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Answer 2

Step-by-step explanation:

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10th

Maths

Real Numbers

Proofs of Irrationality

Prove that √(5) - √(3) is n...

MATHS

Prove that

5

−

3

is not a rational number.

December 26, 2019

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Daizzy Raj

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ANSWER

Let

5

−

3

be a rational number of form

b

a

,where b



=0

Squaring on both sides

(

5

−

3

)

2

=(

b

a

)

2

(

5

)

2

+(

3

)

2

−2(

5

)(

3

)=

b

2

a

2

5+3+2

1

5=

b

2

a

2

8+2

1

5=

b

2

a

2

2

1

5=

b

2

a

2

−8

1

5=

2b

2

a

2

−8b

2

since

1

5 is irrational ,

2b

2

a

2

−8b

2

is rational

Since LHS



= RHS, contradiction arises,

Therefore

5

−

3

is irrational