Math, asked by akshita3439, 1 month ago

prove that root 3 + root 2 is irrational​

Answers

Answered by birju74
0

Answer:

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Answered by ATTITUDEMAYANK
1

Answer:

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Step-by-step explanation:

Answer

Let us assume

3

+

2

be a rational number

3

+

2

=

q

p

, where p,q∈z,q

=0

3

=

q

p

2

By squaring on both sodes, (

3

)

2

=(

q

p

2

)

2

3=

q

2

p

2

−2.

2

.

q

p

+2

2

2

.

q

p

=

q

2

p

2

+2−3

⇒2

2

.

q

p

=

q

2

p

2

−1

2(

2

)

q

p

=

q

2

p

2

−q

2

2

=(

q

2

p

2

−q

2

)(

2p

q

)

2

=

2pq

p

2

−q

2

2

is a rational number ∵

2pq

p

2

−q

2

is rational.

But

2

is not a rational number. This leads us to a contradiction.

∴ our assumption that

3

+

2

, is a ab be rational number is wrong

3

+

2

is an irrational number.

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