Question

show that root 7 is irrational ​

Answer 1

Answer:

this is the answer

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Answer 2

Answer:

Step-by-step explanation:

let us assume that √7 is a rational number

⇒√7 = p/q (where p,q∈ positive  integer,q≠0 and H.C.F(p,q)=1 )

squaring on both sides

⇒7=p²/q²

⇒p²=7 q² →equation 1

here 7 divides p² then 7 divides p

by Euclid division algorithm

p=7 k

substitute p=7 k in equation 1

⇒7² k² = 7 q²

⇒7 k² = q²

7 divides q² then 7 divides q

so p,q has common factor 7

this is wrong

∵H.C.F(p,q) = 1

∴this is our contradiction that √7 is a rational number is wrong

∴√7 is an irrational  number.

hope you understand