October 2018 1 9 Report

1. Doprowadź do najprostszej postaci. Które z podanych liczb są wymierne, a które niewymierne?

a)\frac{2}{\sqrt{2}}-\sqrt{2}+1=

b)\frac{4\sqrt{3}+1}{\sqrt{3}}-\frac{\sqrt{3}}{3}=

c)\frac{-5}{2-\sqrt{3}}+10=

d)\frac{\sqrt{12}-\sqrt{3}}{2}:\frac{2}{\sqrt{3}}=

2.Zastosuj wzory skróconego mnożenia:

a)(4\sqrt{5}+1) ^{2}=

b)(3\sqrt{5}+2) ^{2}=

c)(4\sqrt{5}+5 \sqrt{3}) ^{2}=

d)(\sqrt{5}-1)(1+\sqrt{5})=

e)(3\sqrt{5}-2)(3\sqrt{5}+2)=

f)(\sqrt{5}-2\sqrt{7})(\sqrt{5}+2\sqrt{7})=

g)(\sqrt{3}+\sqrt{2})(\sqrt{2}-\sqrt{3})=

h)(\sqrt{5}-1)^{3}=

i)(\sqrt{3}+4)^{3}=


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