Question

Prove that 7-2 under root 3 is irrational number

Answer 1

Hey user !!

Here is your answer !!
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Let us suppose that 7-2√3 is a rational number
7-2√3=p/q

-2√3=p/q-7

-2√3=(p-7q)/q

√3=(p-7q)/-2q

It is integer /Integer

√3 is an irrational number

It contradicts the fact that 7-2√3 is an irrational number

Hope it is satisfactory :-)
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Answer 2

Heya......^_^

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Here's ur ans. ⬇

To prove 7 - 2√3 is an irrational no.

➡ Let 7-2√3 be a rational no. then it would be in the form of p/q where p and q are integers and q≠0

7-2√3 = p/q

-2√3 = p/q - 7

√3 = -1/2 ( p/q - 7)

We know that ,

-1/2 , p/q ,-7 all are integers , thereby -1/2 (p/q - 7 ) is a rational no.

This means √3 is also a rational no. but it contradicts with the fact that √3 is an irrational no.

Hence , our supposition is wrong

7-2√3 is an irrational no.

HENCE PROVED

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✌Hope it helps