Prove root 5 irrational number in hindi |अपरिमेय_संख्या| class 10 maths

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prove that root 5 is irrational
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prove that √5 is irrational
#provethatroot5isirrational
#proveroot5isirrationalnumber
#सिद्धकीजिए√5अपरिमेय संख्या है
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prove √5 irrational
step 1 Assume √5 is a rational number
so it can be written in the form of p/q where p,q are co-prime numbers (having only one common factors I.e. 1)
▪︎°▪︎ √5=p/q
= q√5=p
Step 2 squaring both sides
5q²=p² -(1)
apply Fundamental theorem of arithmetic
p² is divisible by 5
▪︎°▪︎ p is also divisible by 5
▪︎°▪︎ p=5c -(2) (where c is any number )
put value of p in eqn (1) or from eqn 2 and 1 , we get
5q² = 25p²
q²=5p² -(3) from Fundamental theorem of arithmetic
q² is divisible by 5
also q is divisible by 5
from eqn 1 and 3 ,we get
p and q have another common factor 5
therefore a contradiction arises due to our wrong or incorrect assumption
▪︎°▪︎ √5 is a irrational number
hence proved
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[@ajaythakur2788]

🎉amazing brother

[@SKlassess]

Thank you