Oblicz: Dam naj √28 -√175 +√252 = √392 - √150 +√ 578 - √486= 4√16 - [latex] sqrt[4]625} [/latex] + 3∛27 = 2∛125 + 2∛54 - ∛250=

Oblicz: Dam naj √28 -√175 +√252 = √392 - √150 +√ 578 - √486= 4√16 - [latex] sqrt[4]625} [/latex] + 3∛27 = 2∛125 + 2∛54 - ∛250=
Odpowiedź

[latex]sqrt{28}-sqrt{175}+sqrt{252}=sqrt{4*7}-sqrt{25*7}+sqrt{36*7}=\sqrt{2^{2}*7}-sqrt{5^{2}*7}+sqrt{6^{2}*7}=2sqrt{7}-5sqrt{7}+6sqrt{7}=3sqrt{7}[/latex] [latex]sqrt{392}-sqrt{150}+sqrt{578}-sqrt{486}=\sqrt{196*2}-sqrt{25*6}+sqrt{289*2}-sqrt{81*6}=\sqrt{14^{2}*2}-sqrt{5^{2}*6}+sqrt{17^{2}*2}-sqrt{9^{2}*6}}\14sqrt{2}-5sqrt{6}+17sqrt{2}-9sqrt{6}=31sqrt{2}-14sqrt{6}[/latex] [latex]4sqrt{16}-sqrt[4]{625}+3sqrt[3]{27}=4sqrt{4^{2}}-sqrt[4]{5^{4}}+3sqrt[3]{3^{3}}=4*4-5+3*3=\16-5+9=20 [/latex] [latex]2sqrt[3]{125}+2sqrt[3]{54}-sqrt[3]{250}=2sqrt[3]{5^{3}}+2sqrt[3]{27*2}-sqrt[3]{125*2}=\2*5+2sqrt[3]{3^{3}*2}-sqrt[3]{5^{3}*2}=10+2*3sqrt[3]{2}-5sqrt[3]{2}=\10+6sqrt[3]{2}-5sqrt[3]{2}=10+sqrt[3]{2}[/latex]

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