1)   Vypočtěte:

\displaystyle {{5}^{2}}=

\displaystyle -{{5}^{2}}=

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

\displaystyle {{8}^{2}}=

\displaystyle -{{8}^{2}}=

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

\displaystyle {{13}^{2}}=

\displaystyle -{{13}^{2}}=

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

 

2)   Vypočtěte:

\displaystyle {{4}^{2}}=

\displaystyle -{{5}^{2}}=

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

\displaystyle -{{10}^{2}}=

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

\displaystyle -{{12}^{2}}=

\displaystyle {{11}^{2}}=

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

\displaystyle -{{20}^{2}}=

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

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

\displaystyle -{{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)=

\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}}=

 

 


 

Výsledky:

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

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

3)
1. sloupec:  \displaystyle \ -\frac{1}{4}\ ;\ \frac{9}{25}\ ;\ \frac{25}{4}\ ;
2. sloupec:  \displaystyle \ \frac{9}{21}\ ;\ \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 36;\ 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{49}{81};\ 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)\ 42;\ 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)\ 19;\ i)\ 13;\  \displaystyle j)\ 44;\ k)\ 17;\ l)\ 20;\  \displaystyle m)\ 5;\ n)\ 1;\ o)\ \frac{2}{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)-1;\

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