Question

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How do you show that √7 is irrational ?

{Prove}

Time limit : 7 mins

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✔️50 points✔️

Answers to be given accordingly of class 10 .

Answer 1

Answer:

if u see the answer of root seven it goes on so we can say it is irrational.

as 7 is not a perfect square it's answer comes in a form of decimals and is irrational

hope this is the needed answer

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Answer 2

Step-by-step explanation:

let us assume that √7 be rational.

then it must in the form of p / q.

√7 = p / q

√7 x q = p

squaring on both sides

7q² = p² ------1.

p is divisible by 7

p = 7c [c is a positive integer] [squaring on both sides ]

p²= 49c²

subsitute p² in eqn(1) we get

7q² = 49 c²

q² = 7c²

q is divisble by 7

thus q and p have a common factor 7.

there is a contradiction to our assumption

as our assumsion p & q are co prime but it has a common factor.

so that √7 is an irrational.

hope it helps u ☺️☺️