a)

$\sqrt{3}\cdot \sqrt{75}=\sqrt{3\cdot 75}=\sqrt{225}=15$

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b)

$\sqrt{27}\cdot \sqrt{3}=\sqrt{27\cdot 3}=\sqrt{81}=9$

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c)

$\sqrt{8}\cdot \sqrt{18}=\sqrt{8\cdot 18}=\sqrt{144}=12$

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d)

$\sqrt{54}\cdot \sqrt{6}=\sqrt{9\cdot 6}\cdot \sqrt{6}=\sqrt{9\cdot 6\cdot 6}=\sqrt{9\cdot 36}=\sqrt{9}\cdot \sqrt{36}=3\cdot 6=18$

Inny sposób:

$\sqrt{54}\cdot \sqrt{6}=\sqrt{54\cdot 6}=\sqrt{324}=18$

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e)

$\sqrt{6}\cdot \sqrt{24}=\sqrt{6\cdot 24}=\sqrt{6\cdot 6\cdot 4}=\sqrt{36\cdot 4}=\sqrt{36}\cdot \sqrt{4}=6\cdot 2=12$

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f)

$\sqrt{45}\cdot \sqrt{5}=\sqrt{9\cdot 5}\cdot \sqrt{5}=\sqrt{9\cdot 5\cdot 5}=\sqrt{9\cdot 25}=3\cdot 5=15$

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g)

$\sqrt{5}\cdot \sqrt{20}=\sqrt{5\cdot 20}=\sqrt{100}=10$

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h)

$\sqrt{8}\cdot \sqrt{32}=\sqrt{8\cdot 32}=\sqrt{8\cdot 8\cdot 4}=\sqrt{64}\cdot \sqrt{4}=8\cdot 2=16$

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i)

$\sqrt{320}:\sqrt{5}=\sqrt{320:5}=\sqrt{64}=8$

Inny sposób:

$\sqrt{320}:\sqrt{5}=\sqrt{320:5}=\sqrt{32\cdot 10:5}=\sqrt{32\cdot 2}=\sqrt{64}=8$

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j)

$\sqrt{147}:\sqrt{3}=\sqrt{147:3}=\sqrt{49}=7$

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k)

$\sqrt{68}:\sqrt{17}=\sqrt{68:17}=\sqrt{4}=2$

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l)

$\sqrt{112}:\sqrt{7}=\sqrt{112:7}=\sqrt{16}=4$

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ł)

$\sqrt{243}:\sqrt{3}=\sqrt{243:3}=\sqrt{81}=9$

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m)

$\sqrt{12,5}:\sqrt{0,5}=\sqrt{12,5:0,5}=\sqrt{125:5}=\sqrt{25}=5$

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n)

$\sqrt{324:64}=\sqrt{324}:\sqrt{64}=18:8=\frac{9}{4}$

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o)

$\sqrt{324:144}=\sqrt{324}:\sqrt{144}=18:12=\frac{3}{2}$

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p)

$\sqrt{144:9}=\sqrt{144}:\sqrt{9}=12:3=4$

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r)

$\sqrt{36:16}=\sqrt{36}:\sqrt{16}=6:4=\frac{3}{2}$

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s)

$\sqrt{196:49}=\sqrt{196}:\sqrt{49}=14:7=2$

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t)

$\sqrt{256:25}=\sqrt{256}:\sqrt{25}=16:5=\frac{16}{5}$

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u)

$\sqrt[3]{36}\cdot \sqrt[3]{6}=\sqrt[3]{36\cdot 6}=\sqrt[3]{216}=6$

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w)

$\sqrt[3]{4\frac{17}{27}}=\sqrt[3]{\frac{125}{27}}=\frac{\sqrt[3]{125}}{\sqrt[3]{27}}=\frac{5}{3}$

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y)

$\sqrt[3]{125:8}=\sqrt[3]{125}:\sqrt[3]{8}=5:2=\frac{5}{2}$

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z)

$\sqrt[3]{4}\cdot \sqrt[3]{16}=\sqrt[3]{64}=4$