Examine, whether the following numbers are rational or irrational:
$\frac{10}{2 \sqrt{5}}$

Open in App

Solution

$\frac{10}{2 \sqrt{5}}$
$= \frac{2 \times 5}{2 \sqrt{5}}$
$= \frac{2 \times 5 \div 2}{2 \sqrt{5} \div 2}$
$= \frac{5}{\sqrt{5}}$
$= \frac{\sqrt{5} \times \sqrt{5}}{\sqrt{5}}$
$= \sqrt{5}$
Which a irrational number
Then $\frac{10}{2 \sqrt{5}}$ is an irrational number

Suggest Corrections

Similar questions

(\sqrt{2} + 2)^{2}

(5 - \sqrt{5}) (5 + \sqrt{5})

{(\sqrt{3} + 2)}^{2}

\frac{2 \sqrt{13}}{3 \sqrt{52} - 4 \sqrt{117}}

\sqrt{8} + 4 \sqrt{32} - 6 \sqrt{2}

(3 + \sqrt{3}) + (3 - \sqrt{3})

(5 + \sqrt{5}) (5 - \sqrt{5})

3 + \sqrt{3}

\sqrt{7} - 2

\sqrt[3]{5} \times \sqrt[3]{25}

\sqrt{7} \times \sqrt{343}

\sqrt{\frac{13}{117}}

\sqrt{8} \times \sqrt{2}

Join BYJU'S Learning Program