3.29 Oblicz wartość wyrażenia. 3.30 Oblicz wartość wyrażenia   na jutro zadanie w załączniku 

odpowiedź w załacznikach

[latex]3.29\ a)\sqrt[3]{2000}+sqrt[3]{-432}+sqrt[3]{2}=sqrt[3]{10^3cdot 2} + sqrt[3]{(-6)^3cdot 2}+sqrt[3]{2}=\\=10sqrt[3]{2}-6sqrt[3]{2}+sqrt[3]{2}=5sqrt[3]{2}\\b)\sqrt[3]{375}-sqrt[3]{-192}-sqrt[3]{-81}=sqrt[3]{5^3cdot 3}-sqrt[3]{(-4)^3cdot 3}-sqrt[3]{(-3)^3cdot 3}=\ \=5sqrt[3]{3}+4sqrt[3]{3}+3sqrt[3]{3}=12sqrt[3]{3}\\ c)\sqrt[4]{2}-sqrt[4]{32}+sqrt[4]{162}=sqrt[4]{2}-sqrt[4]{2^4cdot2}+sqrt[4]{3^4cdot 2}=sqrt[4]{2}-2sqrt[4]{2}+3sqrt[4]{2}=\\=2sqrt[4]{2}[/latex] [latex]d)\sqrt[4]{3}+sqrt[4]{48}-sqrt[4]{243}= sqrt[4]{3}+sqrt[4]{2^4cdot 3}-sqrt[4]{3^4cdot 3}=sqrt[4]{3}+2sqrt[4]{3}-3sqrt[4]{3}=0\\e)\2sqrt[3]{-125}+2sqrt[3]{54}-sqrt[3]{-250}=2sqrt[3]{(-5)^3}+2sqrt[3]{3^3cdot2}-sqrt[3]{(-5)^3cdot2}=\\=2cdot (-5) + 2cdot 3sqrt[3]{2}+5sqrt[3]{2}=-10+11sqrt[3]{2}\\ f)\sqrt[4]{16}-2sqrt[4]{2}+sqrt[4]{-(-2)^5}=sqrt[4]{2^4}-2sqrt[4]{2}+sqrt[4]{2^4cdot2}=2-2sqrt[4]{2}+2sqrt[4]{2}=2[/latex] [latex]g)\sqrt{6sqrt{162 cdot 32}cdot sqrt[3]{54}}-sqrt[6]{128}=sqrt{6sqrt{2cdot 81cdot 2cdot 16} cdot sqrt[3]{3^3cdot 2}} -sqrt[6]{2^6cdot2}=\ \=sqrt{6cdot2cdot9cdot4cdot 3sqrt[3]{2}}-2sqrt[6]{2}=sqrt{6cdot6cdot36sqrt[3]{2}}-2sqrt[6]{2}=36sqrt{sqrt[3]{2}}-2sqrt[6]{2}=\\=36sqrt[6]{2}-2sqrt[6]{2}=34sqrt[6]{2}[/latex] [latex]h)\sqrt[3]{10sqrt{8}cdot sqrt{50}cdot sqrt[3]{250cdot 2^2}}+sqrt[3]{-2}=sqrt[3]{10cdot 2sqrt{2}cdot 5sqrt{2}cdot sqrt[3]{5^3cdot 2^3}}+sqrt[3]{-2}=\ \ =sqrt[3]{100cdot2cdot 5cdot2}+sqrt[3]{-2}=sqrt[3]{10^3cdot 2}-sqrt[3]{2}=10sqrt[3]{2}-sqrt[3]{2}=9sqrt[3]{2}[/latex] [latex]3.30\ a)\sqrt{9cdot 16 + 9cdot 4+9cdot 5}=sqrt{9cdot(16+4+5)}=sqrt{9cdot 25}=3cdot5=15\\ b)\sqrt{25cdot 9+14cdot 25+2cdot 25}=sqrt{25cdot(9+14+2)}=sqrt{25cdot 25}=25\\ c)\sqrt[3]{27cdot 2+27cdot 9+27cdot 16}=sqrt[3]{27cdot(2+9+16)}=sqrt[3]{27cdot 27}=3cdot 3=9\\d)\sqrt[3]{15cdot 64+64cdot 3 +9cdot 64}=sqrt[3]{64cdot(15+3+9)}=sqrt[3]{64cdot 27}=4cdot 3=12[/latex] [latex]e)\sqrt{33^2+44^2}=sqrt{(3cdot 11)^2+(4cdot 11)^2}=sqrt{3^2cdot 11^2+4^2cdot 11^2}=\ \=sqrt{11^2cdot(3^2+4^2)}=sqrt{11^2cdot(9+16)}=sqrt{11^2cdot 25}=11cdot 5=55\ \f)\sqrt{15^2cdot 3^2+4^2cdot 15^2}=sqrt{15^2cdot(3^2+4^2)}=sqrt{15^2cdot (9+16)}=\\=sqrt{15^2cdot 25}=15cdot 5=75[/latex] [latex]g)\sqrt{12^2cdot 5^2-12^2cdot 4^2}=sqrt{12^2cdot(5^2-4^2)}=sqrt{12^2cdot 9}=12cdot 3=36\ \h)\sqrt[4]{11^2cdot 9^2+11^2cdot 6^2+2^2cdot 121}=sqrt[4]{11^2cdot 9^2+11^2cdot 6^2+2^2cdot 11^2}=\\=sqrt[4]{11^2cdot(9^2+6^2+2^2)}=sqrt[4]{11^2cdot(81+36+4)} =sqrt[4]{11^2cdot 121}=\\=sqrt[4]{11^2cdot 11^2}=sqrt[4]{11^4}=11[/latex]