Question

prove that root 5 ia an irrationa number

Answer 1

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Answer 2

Answer:

by the method of contradiction .

let us assume that √5 is rational number .

so,

√5 = a÷ b

b√5=a

squaring on both sides

a² = 5b² ---------------------------------------------------------- ( 1 )

if 5 divides a then 5 also divides b

a = 5c

squaring on both sides

a²=25c² -----------------------------------------------------------( 2 )

substitute equation 1 in equation 2

5b²=25c²

b²=5c²

here a,b,c have 5 as common factor

so,

5 is rational number

but √5 is irrational

this contradiction has arrisen due to our incorrect assumption

this contadicts the fact that ,

√5 is irrational