Math, asked by shankar7989372445, 8 months ago

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$1 + \sqrt{3 \: \: is \: \: a \: rational \: number}$

Answers

Answered by thapaavinitika6765

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As √3 is iraational no

so 1+√3 is iraational

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Answered by sakshisingh27

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Hey there,

let us rationalise this term.

then rationalization answer :-√3/3

now see here you know that '3' is rational for sure???

okk so let us now prove that the term root 3 is irrations.

let us assume that √3 is a rational number(contradiction).

now.

we can write it in the form p/q.

so some conditions:- here p and q are integers and q is not equal to 0 and also their hcf is 1.

now .

=> p/q=√3

(squarring)

=> p²/q²=3

=>p²=3q² ;;;;_ >>>> as here p is the factor and q is the multiple of p and respectively..

thus alltering...do the same by keeping a variable in place of q.

so.. now..

3 will be a factor of both p and q which contradicts are statement. that they bioth have a hcf of 1.

so we make a conclusion that although 2 is rational but √3 is irrational.

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Hope this helped u..

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Hope this will help you...

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$1 + \sqrt{3 \: \: is \: \: a \: rational \: number}$