Question

show that √7 is irrational​

Answer 1

Answer:

Step-by-step explanation:

let us assume that √7  as irrational

so ,

√7 = a/b

b√7 = a

squaring on both sides  , we get

7b² = a² -------------------------------------------------------- ( 1  )

if 7 divides a² then it also divides a

so ,

a = 7c

squaring on both sides , we get

a² = 49c²---------------------------------------------------------(  2  )

substitute equation( 1 )in equation (2 )

we get

7b² = 49 c²

b² = 7 c²

here a b and c have 7 as common factor

so 7 is rational number

but ,

√7 is irrational

this contradiction has arisen due to our incorrect assumption

this contradicts the fact that ,

√7 is a irrational number

hope it helps u

Answer 2

Answer:

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