Mocniny a odmocniny

1) Vypočtěte:

$5^{2}=$

$-5^{2}=$

$\left ( -5 \right )^{2}=$

$8^{2}=$

$-8^{2}=$

$\left ( -8 \right )^{2}=$

$13^{2}=$

$-13^{2}=$

$\left ( -13 \right )^{2}=$

2) Vypočtěte:

$4^{2}=$

$-5^{2}=$

$\left ( -9 \right )^{2}=$

$-10^{2}=$

$\left ( -1 \right )^{2}=$

$-12^{2}=$

$11^{2}=$

$\left ( -15 \right )^{2}=$

$-20^{2}=$

$\left ( -14 \right )^{2}=$

$-\left ( -30 \right )^{2}=$

$-13^{2}=$

3) Vypočtěte:

$\displaystyle -{{\left( \frac{1}{2} \right)}^{2}}=$

$\displaystyle {{\left( -\frac{3}{5} \right)}^{2}}=$

$\displaystyle {{\left( -\frac{5}{2} \right)}^{2}}=$

$\displaystyle {{\left( -\frac{3}{7} \right)}^{2}}=$

$\displaystyle {{\left( \frac{1}{6} \right)}^{2}}=$

$\displaystyle -\frac{1}{{{6}^{2}}}=$

$\displaystyle -\frac{{{3}^{2}}}{4}=$

$\displaystyle -\frac{{{\left( -2 \right)}^{2}}}{5}=$

$\displaystyle \frac{-3}{{{\left( -7 \right)}^{2}}}=$

$\displaystyle \frac{{{\left( -9 \right)}^{2}}}{7}=$

$\displaystyle -\frac{{{9}^{2}}}{{{7}^{2}}}=$

$\displaystyle \frac{-9}{{{\left( -7 \right)}^{2}}}=$

4) Vypočtěte:

$\displaystyle 2\cdot {{3}^{2}}=$

$\displaystyle 7\cdot {{0}^{2}}=$

$\displaystyle \frac{1}{2}\cdot {{\left( -\frac{3}{2} \right)}^{2}}=$

$\displaystyle -5\cdot {{3}^{2}}=$

$\displaystyle -3\cdot {{\left( -6 \right)}^{2}}=$

$\displaystyle {{\left( \frac{5}{2} \right)}^{2}}\cdot \left( -\frac{6}{5} \right)=$

$\displaystyle {{\left( -4 \right)}^{2}}\cdot 3=$

$\displaystyle {{\left( -3 \right)}^{2}}\cdot \left( -3 \right)=$

$\displaystyle {{\left( -\frac{7}{10} \right)}^{2}}\cdot \frac{15}{28}=$

5) Vypočtěte:

$\displaystyle a)\quad 3\cdot {{8}^{2}}+6\cdot {{5}^{2}}-3\cdot {{7}^{2}}=$

$\displaystyle b)\quad {{\left( 9-3 \right)}^{2}}-{{\left( 8-2 \right)}^{2}}-{{\left( 7-1 \right)}^{2}}=$

$\displaystyle c)\quad {{\left( 6-3 \right)}^{2}}-{{\left( 9-4 \right)}^{2}}+{{\left( 5-2 \right)}^{2}}=$

$\displaystyle d)\quad {{\left( 6+2 \right)}^{2}}+\left( 6-{{2}^{2}} \right)=$

$\displaystyle e)\quad {{10}^{2}}-{{\left( -8 \right)}^{2}}+{{\left( -4 \right)}^{2}}=$

$\displaystyle f)\quad {{\left( -7 \right)}^{2}}-{{\left( -3 \right)}^{2}}-{{5}^{2}}=$

$\displaystyle g)\quad {{\left( -3 \right)}^{2}}-{{2}^{2}}-{{3}^{2}}-{{\left( -2 \right)}^{2}}=$

$\displaystyle h)\quad {{\left( -6 \right)}^{2}}\cdot 10+\left( -{{2}^{2}}+7 \right)\cdot 8=$

6) Vypočtěte:

$\displaystyle a)\quad {{\left( \frac{1}{2}+\frac{1}{3} \right)}^{2}}=$

$\displaystyle b)\quad {{\left( \frac{4}{5}-\frac{4}{7} \right)}^{2}}=$

$\displaystyle c)\quad {{\left[ {{\left( \frac{1}{3} \right)}^{2}}-{{\left( -\frac{2}{3} \right)}^{2}} \right]}^{2}}=$

$\displaystyle d)\quad {{\left[ \frac{{{5}^{2}}}{{{11}^{{}}}}-\frac{{{3}^{2}}}{11}+\left( -\frac{169}{{{13}^{2}}} \right) \right]}^{2}}=$

7) Vypočtěte:

$\displaystyle a)\quad \frac{{{16}^{2}}-56}{{{10}^{2}}\left( {{4}^{2}}-{{2}^{2}} \right)}=$

$\displaystyle b)\quad {{\left( \frac{{{4}^{2}}-{{5}^{2}}}{{{3}^{2}}} \right)}^{2}}=$

$\displaystyle c)\quad \frac{{{6}^{2}}+{{2}^{2}}}{10{{\left( 4-5 \right)}^{2}}}=$

$\displaystyle d)\quad \frac{{{\left( {{9}^{2}}-60 \right)}^{2}}}{{{7}^{2}}}=$

$\displaystyle e)\quad \frac{{{\left( 10-9 \right)}^{2}}}{{{5}^{2}}\cdot 7-{{12}^{2}}}=$

$\displaystyle f)\quad \frac{{{8}^{2}}-2\cdot {{7}^{2}}}{-{{6}^{2}}+{{\left( -2 \right)}^{2}}}=$

8) Vypočtěte:

$\displaystyle a)\quad {{\left( -4 \right)}^{2}}-{{3}^{2}}+{{\left( -5 \right)}^{2}}-{{\left( -6 \right)}^{2}}=$

$\displaystyle b)\quad {{\left( -3 \right)}^{2}}\cdot {{3}^{2}}-{{\left( -6 \right)}^{2}}\cdot {{\left( -2 \right)}^{2}}=$

$\displaystyle c)\quad \left( {{7}^{2}}-{{6}^{2}} \right)-\left( {{5}^{2}}-{{4}^{2}} \right)=$

$\displaystyle d)\quad \left( {{15}^{2}}-{{12}^{2}} \right)-\left( {{3}^{2}}+{{6}^{2}} \right)=$

$\displaystyle e)\quad {{10}^{2}}-{{9}^{2}}+{{8}^{2}}-{{7}^{2}}+{{6}^{2}}=$

$\displaystyle f)\quad {{7}^{2}}-{{6}^{2}}+{{5}^{2}}-{{4}^{2}}+{{3}^{2}}=$

$\displaystyle g)\quad 3\cdot \left( {{3}^{2}}-{{4}^{2}} \right)+2\cdot \left( {{7}^{2}}-{{5}^{2}}-{{4}^{2}} \right)=$

$\displaystyle h)\quad 2\cdot \left( {{8}^{2}}-{{2}^{2}} \right)-10\cdot \left( {{5}^{2}}-{{3}^{2}} \right)=$

$\displaystyle i)\quad {{\left[ {{12}^{2}}-{{10}^{2}}-{{6}^{2}} \right]}^{2}}=$

$\displaystyle j)\quad {{\left[ {{11}^{2}}+\left( {{11}^{2}}-141 \right)-3\cdot {{5}^{2}} \right]}^{2}}=$

9) Vypočtěte:

$\displaystyle a)\quad {{\left( 8-6 \right)}^{2}}=$

$\displaystyle b)\quad {{\left( 16-19 \right)}^{2}}=$

$\displaystyle c)\quad {{\left( {{12}^{2}}-{{11}^{2}}-4 \right)}^{2}}=$

$\displaystyle d)\quad {{9}^{2}}-\left( {{10}^{2}}-{{5}^{2}} \right)=$

$\displaystyle e)\quad {{12}^{2}}-\left( {{6}^{2}}+{{4}^{2}}\cdot 3 \right)=$

$\displaystyle f)\quad \left( {{5}^{2}}-{{4}^{2}}\cdot 2 \right)^{2}=$

$\displaystyle g)\quad {{\left[ \left( 21+{{7}^{2}} \right)-{{8}^{2}} \right]}^{2}}=$

$\displaystyle h)\quad 2\cdot \left[ \left( 42-{{4}^{2}} \right)\cdot 8-5\cdot {{6}^{2}} \right]=$

$\displaystyle i)\quad {{20}^{2}}-3\cdot \left[ {{11}^{2}}-\left( 70-{{8}^{2}} \right) \right]=$

$\displaystyle j)\quad \frac{{{8}^{2}}-{{6}^{2}}}{{{4}^{2}}-12}=$

10) Vypočtěte:

$\displaystyle\sqrt{\frac{1}{49}}=$

$\displaystyle \sqrt{\frac{1}{144}}=$

$\displaystyle \sqrt{\frac{1}{256}}=$

$\displaystyle \sqrt{\frac{25}{16}}=$

$\displaystyle \sqrt{\frac{36}{49}}=$

$\displaystyle \sqrt{\frac{64}{121}}=$

$\displaystyle \sqrt{\frac{400}{121}}=$

$\displaystyle \sqrt{\frac{169}{324}}=$

$\displaystyle \sqrt{\frac{81}{196}}=$

$\displaystyle \sqrt{\frac{0}{9}}=$

$\displaystyle \sqrt{\frac{49}{324}}=$

$\displaystyle \sqrt{\frac{16}{225}}=$

11) Vypočtěte:

$\displaystyle \sqrt{1600}=$

$\displaystyle \sqrt{4900}=$

$\displaystyle \sqrt{1210000}=$

$\displaystyle \sqrt{1960000}=$

$\displaystyle \sqrt{289000000}=$

$\displaystyle \sqrt{900}=$

$\displaystyle \sqrt{3600}=$

$\displaystyle \sqrt{1440000}=$

$\displaystyle \sqrt{1690000}=$

$\displaystyle \sqrt{256000000}=$

$\displaystyle \sqrt{2500}=$

$\displaystyle \sqrt{6400}=$

$\displaystyle \sqrt{810000}=$

$\displaystyle \sqrt{2250000}=$

$\displaystyle \sqrt{16000000}=$

12) Vypočtěte:

$\displaystyle \sqrt{0,36}=$

$\displaystyle \sqrt{0,09}=$

$\displaystyle \sqrt{0,0064}=$

$\displaystyle \sqrt{0,0324}=$

$\displaystyle \sqrt{0,000256}=$

$\displaystyle \sqrt{0,000196}=$

$\displaystyle \sqrt{0,81}=$

$\displaystyle \sqrt{1,21}=$

$\displaystyle \sqrt{0,0361}=$

$\displaystyle \sqrt{0,0025}=$

$\displaystyle \sqrt{0,000169}=$

$\displaystyle \sqrt{0,000225}=$

13) Vypočtěte:

$\displaystyle a)\quad \sqrt{16}\cdot \sqrt{9}=$

$\displaystyle b)\quad \sqrt{\frac{225}{16}\cdot 256}=$

$\displaystyle c)\quad \sqrt{81\cdot 100}=$

$\displaystyle d)\quad \sqrt{\frac{1}{25}}\cdot \sqrt{\frac{100}{9}}=$

$\displaystyle e)\quad \sqrt{0,36}\cdot \sqrt{0,25}=$

$\displaystyle f)\quad \sqrt{\frac{64}{100}\cdot 400}=$

14) Vypočtěte:

$\displaystyle a)\quad \sqrt{12+4}=$

$\displaystyle b)\quad \sqrt{-8+33}=$

$\displaystyle c)\quad \sqrt{262+27}=$

$\displaystyle d)\quad \sqrt{169-25}=$

$\displaystyle e)\quad \sqrt{81}+\sqrt{25}=$

$\displaystyle f)\quad \sqrt{256}-\sqrt{196}=$

$\displaystyle g)\quad \sqrt{169}-\sqrt{225}=$

$\displaystyle h)\quad \sqrt{361}+\sqrt{1}=$

$\displaystyle i)\quad \sqrt{{{\left( 4+9 \right)}^{2}}}=$

$\displaystyle j)\quad \sqrt{{{\left( 98-54 \right)}^{2}}}=$

$\displaystyle k)\quad \sqrt{{{\left( 17 \right)}^{2}}}=$

$\displaystyle l)\quad \sqrt{20\cdot 20}=$

$\displaystyle m)\quad \frac{50-\sqrt{225}}{\sqrt{49}}=$

$\displaystyle n)\quad \frac{\sqrt{64}\cdot \sqrt{36}}{\sqrt{9}\cdot \sqrt{256}}=$

$\displaystyle o)\quad \frac{\sqrt{36}+\sqrt{9}}{\sqrt{25}\cdot \sqrt{9}}=$

$\displaystyle p)\quad \frac{\sqrt{64}\cdot \sqrt{16}}{\sqrt{4}+\sqrt{36}}=$

15) Vypočtěte:

$\displaystyle a)\quad \sqrt{5\cdot \sqrt{18+\sqrt{49}}}=$

$\displaystyle b)\quad \frac{11}{{{3}^{2}}}+\frac{{{13}^{2}}}{\sqrt{81}}+\sqrt{36}=$

$\displaystyle c)\quad \sqrt{40-\sqrt{5+{{3}^{2}}+2}}=$

$\displaystyle d)\quad \sqrt{\frac{{{1}^{2}}}{12}+\frac{\sqrt{225}}{{{12}^{2}}}+\frac{37}{144}}=$

$\displaystyle e)\quad \sqrt{\sqrt{121}+\sqrt{{{3}^{2}}+{{4}^{2}}}}=$

$\displaystyle f)\quad \sqrt{\frac{25}{36}}-\sqrt{\frac{9}{4}}-\sqrt{\frac{121}{9}}=$

16) Vypočtěte:

$\displaystyle a)\quad \sqrt{4\cdot 7+36}=$

$\displaystyle b)\quad \sqrt{11\cdot 8-7}=$

$\displaystyle c)\quad \sqrt{443-27\cdot 5+16}=$

$\displaystyle d)\quad \sqrt{{{3}^{2}}+{{5}^{2}}+15}=$

$\displaystyle e)\quad \sqrt{{{4}^{2}}\cdot {{1}^{2}}+65}=$

$\displaystyle f)\quad \sqrt{144}+\sqrt{225}-\sqrt{324}=$

$\displaystyle g)\quad \sqrt{4\cdot 4\cdot 4\cdot 4}=$

$\displaystyle h)\quad \sqrt{121}\cdot \sqrt{64}\cdot \sqrt{9}=$

$\displaystyle i)\quad \sqrt{324}-\sqrt{16}\cdot \sqrt{25}=$

17) Vypočtěte:

$\displaystyle a)\quad \sqrt{9}+\sqrt{16}-\sqrt{196}+\sqrt{64}=$

$\displaystyle b)\quad \frac{\sqrt{225}-\sqrt{144}}{\sqrt{169}-\sqrt{100}}=$

$\displaystyle c)\quad \frac{\sqrt{{{\left( 9-4+6-5 \right)}^{2}}}}{\sqrt{121}-\sqrt{64}}=$

$\displaystyle d)\quad \frac{\sqrt{259-34}-\sqrt{114+55}}{3\cdot \sqrt{81-72}}=$

$\displaystyle e)\quad \frac{\sqrt{70-3\cdot \left( 2+5\cdot 20 \right)}}{\sqrt{64}-\sqrt{49}- \sqrt{1}}=$

$\displaystyle f)\quad \frac{\sqrt{45}\cdot \sqrt{5}-\sqrt{144+52}}{1+\sqrt{1}+\sqrt{2}\cdot \sqrt{8}-\sqrt{25}}=$

18) Vypočtěte:

$a) \left ( \sqrt{\frac{64}{81}}-\frac{2}{3} \right )^{2}:\frac{2}{9}=$

$c)\; 2:\left ( -\frac{1}{2} \right )^{2}+\frac{6}{\sqrt{25}}\cdot \frac{5}{12}=$

$e) \left ( \sqrt{\frac{1}{4}}+\sqrt{\frac{1}{9}} \right )^{2}:\left ( \frac{1}{3}-\frac{2}{9} \right )=$

$b) \left ( -\frac{1}{4} \right )^{2}-\frac{1}{5}:\sqrt{\frac{9}{100}}+1\frac{1}{2}=$

$d) \, \sqrt{5\frac{4}{9}}:\left [ \left ( \frac{1}{3} \right )^{2}-\sqrt{\frac{1}{4}} \right ]=$

$f) \, 3,3-\sqrt{\frac{9}{25}}\cdot \left ( 7\frac{1}{2}-3\frac{1}{3} \right )=$

19) Vypočtěte:

$a) \, \frac{\frac{2}{5}\cdot 0,5+\left ( \frac{1}{4} \right )^{2}:\frac{3}{8}}{\frac{1}{6}\cdot \left ( -\frac{1}{4} \right )^{2}}=$	$b)\, \frac{2\frac{1}{3}-\left ( \frac{5}{7} \right )^{2}:\frac{3}{14}}{\frac{1}{3}\cdot \sqrt{\frac{1}{64}}}=$
$c)\, \frac{\frac{1}{6}\cdot \sqrt{0,01}+\frac{3}{5}:\left ( -1\frac{5}{7} \right )}{\frac{3}{7}\cdot \sqrt{2,25}}=$	$d)\, \frac{\left ( -1\frac{1}{3} \right )^{2}-\frac{5}{6}\cdot 0,3}{\frac{5}{9}-\sqrt{2\frac{7}{9}}}=$
$e)\, \frac{\frac{2}{\sqrt{49}}+\frac{8}{9}\cdot 0,5^{2}}{3\frac{1}{3}:1\frac{2}{5}-2}=$	$f)\, \frac{\frac{1}{\sqrt{25}}-\left ( \sqrt{0,09}- \sqrt{\frac{1}{16}}\right )}{\left ( -\frac{4}{5} \right ):\left ( \frac{7}{9}-\frac{11}{18} \right )}=$
$g)\, \frac{\sqrt{0,04}:\left ( \frac{2}{3}-\frac{1}{5} \right )-\frac{3}{7}}{\frac{8}{11}-\left ( -\frac{1}{2} \right )^{2}+\frac{13}{22}}=$	$h)\, \frac{\left [ \frac{1}{9}-\left ( \frac{5}{6} \right )^{2} \right ]:\left ( -\frac{2}{3} \right )}{\frac{2}{3}\cdot 0,25-\sqrt{\frac{9}{16}}}=$
$i)\, \frac{\left ( \frac{1}{4} \right )^{2}\cdot 2\frac{2}{3}-1\frac{1}{2}\cdot \frac{\sqrt{9}}{5}}{\frac{2}{3}-0,5^{2}\cdot \left ( -\frac{2}{5} \right )}=$	$j)\, \frac{\left [ \frac{2}{\sqrt{25}}+\left ( -\frac{1}{6} \right ) \right ]:0,1}{1-\frac{\left ( -4 \right )^{2}}{9}\cdot 0,6}=$

Výsledky:

1)
1. sloupec: 25; -25; 25;
2. sloupec: 64; -64; 64;
3. sloupec: 169; -169; 169;

2)
1. sloupec: 16; -25; 81; -100
2. sloupec: 1; -144; 121; 225
3. sloupec: -400; 196; -900; -169;

3)
1. sloupec: $\displaystyle -\frac{1}{4} ; \frac{9}{25} ; \frac{25}{4} ;$ 2. sloupec: $\displaystyle \frac{9}{49} ; \frac{1}{36} ; -\frac{1}{36} ;$ 3. sloupec: $\displaystyle -\frac{9}{4} ; -\frac{4}{5} ; \frac{-3}{21} ;$ 4. sloupec: $\displaystyle \frac{81}{7} ; -\frac{81}{49} ; -\frac{9}{49} ;$

4)
1. sloupec: $\displaystyle 18; 0; \frac{9}{8};$ 2. sloupec: $\displaystyle -45; -108; -\frac{15}{2};$ 3. sloupec: $\displaystyle 48; -27; \frac{21}{80};$

5) $\displaystyle a) 195; b) -36; c) -7; d) 66; e) 52; f) 15; g) -8; h) 384;$

6) $\displaystyle a) \frac{25}{36}; b) \frac{64}{1225}; c) \frac{1}{9}; d) \frac{25}{121};$

7) $\displaystyle a) \frac{1}{6}; b) 1; c) 4; d) 9; e) \frac{1}{31}; f) 1\frac{1}{16};$

8) $\displaystyle a) -4; b) -63; c) 4; d) 36; e) 70; f) 31; g) -5; h) -40; i) 64; j) 676;$

9) $\displaystyle a) 4; b) 9; c) 361; d) 6; e) 60; f) 49; g) 36; h) 56; i) 55; j) 7;$

10)
1. sloupec: $\displaystyle \frac{1}{7}; \frac{1}{12}; \frac{1}{16};$ 2. sloupec: $\displaystyle \frac{5}{4}; \frac{6}{7}; \frac{8}{11};$ 3. sloupec: $\displaystyle \frac{20}{11}; \frac{13}{18}; \frac{9}{14};$ 4. sloupec: $\displaystyle 0; \frac{7}{18}; \frac{4}{15};$

11)
1. sloupec: 40; 70; 1100; 1400; 17000;
2. sloupec: 30; 60; 1200; 1300; 16000;
3. sloupec: 50; 80; 900; 1500; 4000;

12)
1. sloupec: 0,6; 0,3; 0,08;
2. sloupec: 0,18; 0,016; 0,014;
3. sloupec: 0,9; 1,1; 0,19;
4. sloupec: 0,05; 0,013; 0,015;

13) $\displaystyle a) 12; b) 60; c) 90;$ $\displaystyle d) \frac{2}{3}; e) 0,3; f) 16;$

14) $\displaystyle a) 4; b) 5; c) 17;$ $\displaystyle d) 12; e) 14; f) 2;$ $\displaystyle g)-2; h) 20; i) 13;$ $\displaystyle j) 44; k) 17; l) 20;$ $\displaystyle m) 5; n) 1; o) frac{3}{5}; p) 4;$

15) $\displaystyle a) 5; b) 26; c) 6;$ $\displaystyle d) \frac{2}{3}; e) 4; f)-\frac{13}{3};$

16) $\displaystyle a) 8; b) 9; c) 18;$ $\displaystyle d) 7; e) 9; f) 9;$ $\displaystyle g) 16; h) 264; i)-2;$

17) $\displaystyle a) 1; b) 1; c) 2; d) \frac{2}{9}; e)$ nelze řešit (pod odmocninou vyjde záporné číslo); $\displaystyle f) 1;$

18) $a) \frac{2}{9};\, b) \frac{43}{48};\, c) 8\frac{1}{2};\, d)-6;\, e) 6\frac{1}{4};\, f)\frac{4}{5}$

19) $a)\, 13\frac{3}{4};\, b) -1\frac{1}{7};\, c) -\frac{14}{27};\, d) -1\frac{3}{8};\, e) 1\frac{1}{3};\, f) -\frac{1}{32};\, g) 0; \, h) -1\frac{1}{2};\, i) -\frac{22}{23};\, j) -35$

Výsledky:

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