Show that root 7 is irrational …

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Show that root 7 is irrational number

Posted by 𝖄𝓸𝓰𝓲𝓽𝓪♛🖤😎 𝒴𝒶𝒹𝓊𝓋𝒶𝓃𝓈𝒽𝒾🔥🔥 6 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 1 month ago

let us assume that √7 be rational.
then it must in the form of p / q [q ≠ 0] [p and q are co-prime]
√7 = p / q
=> √7 x q = p
squaring on both sides
=> 7q²= p² ------ (1)
p² is divisible by 7
p is divisible by 7
p = 7c [c is a positive integer] [squaring on both sides ]
p² = 49 c² --------- (2)
Subsitute p² in equ (1) we get
7q² = 49 c²
q² = 7c²
=> q is divisible by 7
thus q and p have a common factor 7.
there is a contradiction
as our assumsion p & q are co prime but it has a common factor.
So that √7 is an irrational.

3Thank You

ANSWER

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CBSE > Class 10 > Mathematics