Question

2. Prove that
$\frac{1}{ \sqrt{7} } \: is \: irrational.$

Standard:- 10

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Answer 1

Heya User ✌

Here's your answer friend,

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==> Let 1/√7 be a rational number.

$therefore$
==> 1/√7 = a/b .........{where b ≠ 0 and a and b are coprime numbers }

==> b = √7a

==> b/a = √7

since,

a and b are integers

therefore,

==> b/a is a rational number.


but,

√7 is an irrational number.

therefore,

➡Our assumption proved wrong.

√7 is an irrational number.

Hence,

✔ 1/√7 is an irrational number.

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HOPE IT HELPS YOU :)

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Answer 2

$Heya$‼

$Let\: \frac{1}{ \sqrt{7} } \: is \: a \: rational \: number.$

$\frac{1}{ \sqrt{7} } =\frac{a}{b}$ , where a and b are integers and (b ≠ 0).

$\sqrt{7}=\frac{b}{a}$

Since $b/a$ is a rational number so, $\sqrt{7}$ is also a rational number.

But this contradicts the fact that $\sqrt{7}$ is an irrational number.

Thus, our incorrect consumption is wrong.

So, we include that $\frac{1}{ \sqrt{7} }$ is irrational.
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