Question

Prove that 2root3/5 is an irrational

Answer 1

$\huge{\underline{\underline{\mathcal{\blue{ANSWER:-}}}}}$

Let $\frac{2 \sqrt{3} }{5}$be a rational no. which can be written in the form of $\frac{p}{q}$

$\longrightarrow$$\frac{2 \sqrt{3} }{5} = \frac{p}{q}$

$\longrightarrow$$\sqrt{3} = \frac{5p}{2q}$

$\longrightarrow$$\frac{5p}{2q} is \: a \: rational \: no.$

$but \: \sqrt{3} is \: an \: irrational \: no.$

Thus,$\frac{2 \sqrt{3} }{5}$is an irrational number.

$\huge{\underline{\underline{\mathfrak{\blue{THANKS}}}}}$

Answer 2

$</p><p>Let \frac{2 \sqrt{3} }{5} </p><p>5</p><p>2 </p><p>3</p><p> </p><p> </p><p> </p><p><strong><em> written in the form of</em></strong> \frac{p}{q} </p><p>q</p><p>p</p><p> </p><p> </p><p></p><p>⟶ \frac{2 \sqrt{3} }{5} = \frac{p}{q} </p><p>5</p><p>2 </p><p>3</p><p> </p><p> </p><p> </p><p> = </p><p>q</p><p>p</p><p> </p><p> </p><p></p><p>⟶ \sqrt{3} = \frac{5p}{2q} </p><p>3</p><p> </p><p> = </p><p>2q</p><p>5p</p><p> </p><p> </p><p></p><p>⟶ \frac{5p}{2q} is \: a \: rational \: no. </p><p>2q</p><p>5p</p><p> </p><p> <strong><em>isarationalno</em></strong>.</p><p></p><p>but \: \sqrt{3} is \: an \: irrational \: no.but </p><p>3</p><p> </p><p> <strong><em>isanirrationalno</em></strong>.</p><p></p><p>Thus,\frac{2 \sqrt{3} }{5} </p><p>5</p><p>2 </p><p>3</p><p> </p><p> </p><p> </p><p><strong><em> is an irrational number.</em></strong></p><p></p><p>\huge{\underline{\underline{\mathcal{\green{HOPE \ ITS \ HELP \ YOU}}}}}$