Rozwiąż test z Pierwiastków (łatwy)(załącznik) proszę o obliczenia każde zadanie się liczy

zad. 1 a) [latex]sqrt{frac{9}{25}}=frac{sqrt{9}}{sqrt{25}}=frac{3}{5}[/latex] b) [latex]sqrt{5}*sqrt{2}*sqrt{10}=sqrt{2*5*10}=sqrt{100}=10[/latex] c) [latex]sqrt{4900}=sqrt{100*49}=sqrt{100}*sqrt{49}=10*7=70[/latex] d) [latex]sqrt{1frac{11}{25}}=sqrt{frac{36}{25}}=frac{sqrt{36}}{sqrt{25}}=frac{6}{5}=1frac{1}{5}[/latex] e) [latex]sqrt{20*5}=sqrt{100}=10[/latex] f) [latex]sqrt{100*625}=sqrt{100}*sqrt{625}=10*25=250[/latex] zad. 2 a) [latex]a) sqrt{64} + sqrt[3]{125}=8+5=13[/latex] b) [latex]5sqrt{7}*sqrt{5frac{1}{7}}=sqrt{25*7}*sqrt{frac{36}{7}}=sqrt{25* ot7*frac{36}{ ot7}}=sqrt{25*36}=5*6=30[/latex] c) [latex]sqrt{sqrt{25}-sqrt{16}}=sqrt{5-4}=sqrt{1}=1[/latex] d) [latex]sqrt{3*sqrt{3*sqrt{9}}}=sqrt{3*sqrt{3*3}}=sqrt{3*sqrt{9}}=sqrt{3*3}=sqrt{9}=3[/latex] e) [latex]sqrt{13^2}+sqrt[3]{7^3}=13+7=20[/latex] f) [latex]sqrt{5frac{2}{3}}:sqrt{2frac{1}{25}}=sqrt{frac{17}{3}}:sqrt{frac{51}{25}}=sqrt{frac{ ot{17}^1}{3}*frac{25}{ ot{51}_3}}=sqrt{frac{25}{9}}=frac{sqrt{25}}{sqrt{9}}=frac{5}{3}=1frac{2}{3}[/latex] g) [latex]5sqrt{7}*sqrt{7}=5*7=35[/latex] h) [latex]frac{sqrt{2}*sqrt{6}}{sqrt{3}}=sqrt{frac{2*6}{3}}=sqrt{frac{12}{3}}=sqrt{4}=2[/latex] i) [latex]sqrt{32}:sqrt{2}=sqrt{32:2}=sqrt{16}=4[/latex] j) [latex]sqrt{5}*sqrt{20}+sqrt[3]{54}:sqrt[3]{2}=sqrt{5*20}+sqrt[3]{54:2}=sqrt{100}+sqrt[3]{27}=10+3=13[/latex] zad. 3 a) [latex]sqrt{9a^2}=sqrt{9}*sqrt{a^2}=3a[/latex] b) [latex]sqrt[3]{frac{27a^3}{64}}=frac{sqrt[3]{27a^3}}{sqrt[3]{64}}=frac{sqrt[3]{27}*sqrt[3]{a^3}}{4}=frac{3a}{4}=frac{3}{4}a[/latex] c) [latex]sqrt{36a^2b^6c^{12}}=sqrt{6^2 * a^2 * (b^3)^2 * (c^6)^2}=6ab^3c^6[/latex] zad. 4 a) [latex]sqrt{27}=sqrt{9*3}=3sqrt{3}[/latex] b) [latex]sqrt[3]{250}=sqrt[3]{125*2}=5sqrt[3]{2}[/latex] c) [latex]sqrt{16a^4b^2c}=sqrt{4^2*(a^2)^2*b^2*c}=4a^2b sqrt{c}[/latex] zad. 5 a) [latex]3sqrt{7}=sqrt{3^2*7}=sqrt{9*7}=sqrt{63}[/latex] b) [latex]2sqrt[3]{5}=sqrt[3]{2^3*5}=sqrt[3]{8*5}=sqrt[3]{40}[/latex] zad. 6 a) [latex]frac{sqrt{27}+sqrt{3}}{sqrt{108}}=frac{sqrt{9*3}+sqrt{3}}{sqrt{36*3}}=frac{3sqrt{3}+sqrt{3}}{6sqrt{3}}=frac{4sqrt{3}}{6sqrt{3}}=frac{4}{6}=frac{2}{3}[/latex] b) [latex]2sqrt{2}+sqrt{32}-3sqrt{50}=2sqrt{2}+sqrt{16*2}-3sqrt{25*2}=2sqrt{2}+4sqrt{2}-15sqrt{2}=[/latex] [latex]-9sqrt{2}[/latex] zad. 7 a) [latex]frac{5}{sqrt{5}}=frac{5}{sqrt{5}}*frac{sqrt{5}}{sqrt{5}}=frac{5sqrt{5}}{5}=sqrt{5}[/latex] b) [latex]frac{5sqrt{7}}{2sqrt{2}}=frac{5sqrt{7}}{2sqrt{2}}*frac{sqrt{2}}{sqrt{2}}=frac{5*sqrt{7*2}}{2*2}=frac{5sqrt{14}}{4}[/latex] c) [latex]frac{7}{sqrt[3]{3}}=frac{7}{sqrt[3]{3}}*frac{sqrt[3]{9}}{sqrt[3]{9}}=frac{7sqrt[3]{9}}{sqrt[3]{27}}=frac{7sqrt[3]{9}}{3}[/latex] d) [latex]frac{sqrt{3}-1}{2sqrt{5}}=frac{sqrt{3}-1}{2sqrt{5}}*frac{sqrt{5}}{sqrt{5}}=frac{sqrt{3*5}-sqrt{5}}{2*5}=frac{sqrt{15}-sqrt{5}}{10}[/latex] zad. dodatkowe a) [latex]sqrt{2} = frac{1}{2} sqrt{a}[/latex] /*2 [latex]2sqrt{2}=sqrt{a}[/latex] /^2 [latex](sqrt{a})^2= (2sqrt{2})^2[/latex] [latex]a= 4*2[/latex] [latex]a=8[/latex] b) [latex]2sqrt{3}=3sqrt{b}[/latex] /:3 [latex]frac{2}{3}sqrt{3}=sqrt{b}[/latex] /^2 [latex](sqrt{b})^2 = (frac{2}{3}sqrt{3})^2[/latex] [latex]b =frac{4}{9}*3[/latex] [latex]b =frac{4}{3}[/latex] [latex]b=1frac{1}{3}[/latex] c) [latex]frac{3}{2} sqrt[3]{3}=3sqrt[3]{c}[/latex] /:3 [latex]frac{3}{2}*frac{1}{3} * sqrt[3]{3}=sqrt[3]{c}[/latex] [latex]frac{1}{2} * sqrt[3]{3}=sqrt[3]{c}[/latex] /^3 [latex](sqrt[3]{c})^3=(frac{1}{2}sqrt[3]{3})^3[/latex] [latex]c=frac{1}{8}*3[/latex] [latex]c=frac{3}{8}[/latex]