$\sqrt{\frac{1}{3}} = \frac{1}{3} \sqrt{3}$ en ook $\sqrt{\frac{1}{2}} = \frac{1}{2} \sqrt{2}$

$\sqrt{\frac{1}{3}} = \sqrt{\frac{3}{9}} = \sqrt{\frac{1}{9}} \cdot \sqrt{3} = \frac{1}{3} \sqrt{3}$

Ze zijn elkaars omgekeerde, want $\sqrt{\frac{1}{n} \cdot} \sqrt{n} = \sqrt{\frac{1}{n} \cdot n} = \sqrt{1} = 1$ .

$\sqrt{\frac{2}{7}} = \sqrt{\frac{14}{49}} = \sqrt{\frac{1}{49}} \cdot \sqrt{14} = \frac{1}{7} \sqrt{14}$

$\sqrt{\frac{30}{10}} = \sqrt{\frac{30}{100}} = \sqrt{\frac{1}{100}} \cdot \sqrt{30} = \frac{1}{10} \sqrt{30}$

$\sqrt{\frac{1}{8}} = \sqrt{\frac{2}{16}} = \sqrt{\frac{1}{16}} \cdot \sqrt{2} = \frac{1}{4} \sqrt{2}$

$\sqrt{\frac{1}{2}} = \sqrt{\frac{2}{4}} = \sqrt{\frac{1}{4}} \cdot \sqrt{2} = \frac{1}{2} \sqrt{2}$
$\sqrt{4 \frac{1}{2}} = \sqrt{\frac{18}{4}} = \sqrt{\frac{1}{4}} \cdot \sqrt{18} = \frac{1}{2} \cdot \sqrt{9} \cdot \sqrt{2} = \frac{3}{2} \sqrt{2}$
$\sqrt{12 \frac{1}{2}} = \sqrt{\frac{50}{4}} = \sqrt{\frac{1}{4}} \cdot \sqrt{50} = \frac{1}{2} \cdot \sqrt{25} \cdot \sqrt{2} = \frac{5}{2} \sqrt{2}$ en
$\sqrt{24 \frac{1}{2}} = \sqrt{\frac{98}{4}} = \sqrt{\frac{1}{4}} \cdot \sqrt{98} = \frac{1}{2} \cdot \sqrt{49} \cdot \sqrt{2} = \frac{7}{2} \sqrt{2}$ , dus
$\frac{1}{2} \sqrt{2} + \frac{3}{2} \sqrt{2} + \frac{5}{2} \sqrt{2} + \frac{7}{2} \sqrt{2} = \frac{16}{2} \sqrt{2} = 8 \sqrt{2}$ .

$\sqrt{3} + 2 \sqrt{3} = 3 \sqrt{3}$	$\sqrt{36} = 6$
$5 \sqrt{2} + 2 \cdot 2 \sqrt{2} = 9 \sqrt{2}$	$10 \cdot 4 = 40$
$2 \sqrt{5} + 4 \sqrt{5} = 6 \sqrt{5}$	$\sqrt{1600} = 40$
kan niet eenvoudiger	$\sqrt{20} = \sqrt{4} \cdot \sqrt{5} = 2 \sqrt{5}$

$\sqrt{6} + \sqrt{\frac{6}{9}} = \sqrt{6} + \frac{1}{3} \sqrt{6} = 1 \frac{1}{3} \sqrt{6}$

$\sqrt{\frac{6}{9}} + \sqrt{\frac{24}{9}} = \frac{1}{3} \sqrt{6} + \frac{1}{3} \sqrt{24} = \frac{1}{3} \sqrt{6} + \frac{2}{3} \sqrt{6} = \sqrt{6}$

$\sqrt{12} \cdot \sqrt{12} = 12$

$\sqrt{1} = 1$

$2 \sqrt{\frac{2}{3}} = \sqrt{4} \cdot \sqrt{\frac{2}{3}} = \sqrt{4 \cdot \frac{2}{3}} = \sqrt{\frac{8}{3}} = \sqrt{2 \frac{2}{3}}$

$3 \sqrt{\frac{3}{8}} = \sqrt{9} \cdot \sqrt{\frac{3}{8}} = \sqrt{9 \cdot \frac{3}{8}} = \sqrt{\frac{27}{8}} = \sqrt{3 \frac{3}{8}}$

$\sqrt{\sqrt{5} - 1} \cdot \sqrt{\sqrt{5} + 1} = \sqrt{(\sqrt{5} - 1) \cdot (\sqrt{5} + 1)} = \sqrt{5 - 1} = \sqrt{4} = 2$

$2$ ; $4$ ; $2$

$\sqrt{16} = 4$	$\sqrt{64} = 8$
$\sqrt{100} = 10$	$\sqrt{\frac{1}{10.000}} = \frac{1}{100}$

$10 \sqrt{10}$	$\sqrt{100} \cdot \sqrt{2} : \sqrt{5} = \sqrt{40} = \sqrt{4} \cdot \sqrt{10} = 2 \sqrt{10}$
$10 \cdot 2 = 20$	$10$
$100$	$2$

$8 \sqrt{6}$	$2 \sqrt{3} + 2 \sqrt{3} = 4 \sqrt{3}$
$2 \sqrt{6}$	$2 \sqrt{3} - 2 \sqrt{3} = 0$
$15 \cdot 6 = 90$	$2 \sqrt{3} \cdot 2 \sqrt{3} = 4 \cdot 3 = 12$
$\frac{5}{3} = 1 \frac{2}{3}$	$2 \sqrt{3} : 2 \sqrt{3} = 1$

$3 \sqrt{5} + 2 \sqrt{5} = 5 \sqrt{5}$	$3 \sqrt{11} + 2 \sqrt{11} = 5 \sqrt{11}$
$\sqrt{5}$	$3 \sqrt{11} - 2 \sqrt{11} = \sqrt{11}$
$3 \cdot \sqrt{100} = 3 \cdot 10 = 30$	$3 \sqrt{11} \cdot 2 \sqrt{11} = 6 \cdot 11 = 66$
$3 \sqrt{5} : 2 \sqrt{5} = \frac{3}{2} = 1 \frac{1}{2}$	$3 \sqrt{11} : 2 \sqrt{11} = \frac{3}{2} = 1 \frac{1}{2}$

$\sqrt{3}$	$\sqrt{\frac{1}{2}} = \frac{1}{2} \sqrt{2}$	$\sqrt{7}$
$\sqrt{4} = 2$	$\sqrt{\frac{1}{4}} = \frac{1}{2}$	$\sqrt{\frac{1}{2}} = \frac{1}{2} \sqrt{2}$

Linkerkolom:
$\frac{1}{2} \sqrt{2} + 2 \sqrt{2} = 2 \frac{1}{2} \sqrt{2}$
$\sqrt{\frac{6}{9}} + 2 \sqrt{6} = \frac{1}{3} \sqrt{6} + 2 \sqrt{6} = 2 \frac{1}{3} \sqrt{6}$
$2 \sqrt{14} + \sqrt{\frac{14}{49}} = 2 \sqrt{14} + \frac{1}{7} \sqrt{14} = 2 \frac{1}{7} \sqrt{14}$

Rechterkolom:
$\sqrt{\frac{6}{10}} = \sqrt{\frac{60}{100}} = \frac{1}{10} \sqrt{60} = \frac{1}{5} \sqrt{15}$
$\sqrt{36} = 6$
$0,8 - 0,6 = 0,2$

10s

11s

Linkerkolom:
$\sqrt{2^{6} \cdot 3^{4}} = 2^{3} \cdot 3^{2} = 8 \cdot 9 = 72$
$\sqrt{2^{4} \cdot 3^{5}} = 2^{2} \cdot 3^{2} \cdot \sqrt{3} = 4 \cdot 9 \cdot \sqrt{3} = 36 \sqrt{3}$
$\sqrt{2^{4} \cdot 3^{5} \cdot 5^{3}} = 2^{2} \cdot 3^{2} \cdot \sqrt{3} \cdot 5 \cdot \sqrt{5} = 180 \sqrt{15}$

Rechterkolom:
$\sqrt{2^{5} \cdot 3^{5}} = 2^{2} \cdot \sqrt{2} \cdot 3^{2} \cdot \sqrt{3} = 36 \sqrt{6}$
$\sqrt{2^{6} \cdot 3^{5}} = 2^{3} \cdot 3^{2} \cdot \sqrt{3} = 8 \cdot 9 \cdot \sqrt{3} = 72 \sqrt{3}$
$\sqrt{\frac{2^{5}}{3^{4}}} = \frac{2^{2} \cdot \sqrt{2}}{3^{2}} = \frac{4}{9} \sqrt{2}$