Find how many are irrational

Number Theory Level 2

How many of these are irrational numbers?

$\sqrt{\dfrac{16}{36}}$
$\sqrt{\dfrac{27}{48}}$
$\sqrt{\dfrac{18}{17}}$
$0.24\overline{56}$
$\sqrt{\dfrac{37}{68}}$
$\sqrt{\dfrac{50}{2}}$

1 3 2 0 5 4 6

1 solution

Munem Shahriar
Feb 25, 2018

$\sqrt{\dfrac{16}{36}} = \dfrac 46,$ which is a rational number.

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$\sqrt{\dfrac{27}{48}} = \sqrt{\dfrac 9{16}} = \dfrac 34,$ which is a rational number.

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$0.24\overline{56} = \dfrac{2456 - 24}{9900} = \dfrac{2432}{9900},$ which is a rational number.

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$\sqrt{\dfrac{50}2} = \sqrt{25} = 5,$ which is a rational number.

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$\sqrt{\dfrac{18}{17}} = \dfrac{3 \sqrt{2}}{\sqrt{17}},$ which is an irrational number.

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$\sqrt{\dfrac{37}{68}} = \dfrac{\sqrt{37}}{2\sqrt{17}},$ which is an irrational number.

So, the answer is $\boxed{2}$