1.a)√40 * √10b) √12 : √3c)√800 : √2d)√800 * √22.a (∛7) * ∛7b ∛4 * ∛2c ∛5 * ∛25d ∛81 | ∛3 (

Kerep69

a)√40 * √10 =

= √(4*10)*√10 =

= √4*√10*√10 =

= 2*(√10)² =

= 2*10 =

= 20

b) √12 : √3 =

=√(4*3) : √3 =

= √4*√3 :√3 =

= 2√3 : √3 =

= 2

c)√800 : √2=

= √(400*2) : √2 =

= √400*√2 :√2 =

= 20√2 : √2 =

= 20

d)√800 * √2=

= √(400*2) *√2 =

= √400*√2 *√2 =

= 20√2 * √2 =

= 20*(√2)² =

= 20*2=

= 40

a (∛7) * ∛7=

= ∛(7*7 )=

= ∛49

b ∛4 * ∛2 =

= ∛(4*2) =

=∛8 =

c) ∛5 * ∛25 =

= ∛(5*25)=

= ∛125 =

= 5

d ∛81 | ∛3 ( | - oznacza kreskę ułamkową)

=∛(27*3) : ∛3 =

= ∛27*∛3 : ∛3 =

= 3∛3 : ∛3 =

= 3

e ∛4 * ∛6 | ∛3 =

= ∛(4*6) : ∛3 =

= ∛24 : ∛3 =

= ∛(8*3) : ∛3 =

= ∛8*∛3 : ∛3 =

= 2∛3 :∛3 =

= 2

f ∛2 | ∛3 * ∛81 =

= ∛2 : [∛3*∛(27*3) ] =

= ∛2 : [ ∛3 *∛27*∛3] =

= ∛2 : [ ∛3 *3∛3] =

= ∛2 : 3∛9 =

= ⅓*∛(2/9)

3.wyłącz czynnik przed znak pierwiastka i uprość wyrazenie:

a. √200 - √32 + √50 =

√(100*2 -√(16*2) + √(25*2) =

= √100*√2 -√16*√2 +√25*√2 =

= 10√2 -4√2 + 5√2 =

= 11√2

b. 2 √48 - 3 √12 =

=2*√(16*3) -3*√(4*3) =

= 2*√16*√3 -3*√4*√3 =

= 2*4*√3 -3*2*√3 =

= 8√3 -6√3 =

= 2√3

c. √50 + √24 - √18 + √54 =

= √(25*2) + √(4*6) -√(9*2) +√(9*6) =

= √25*√2 +√4*√6 -√9*√2 +√9*√6 =

= 5√2 +2√6 -3√2 +3√6 =

= 2√2 +5√6

4. ZNAJDŹ LICZBĘ której 68 % wynosi

√2¼ + (3 + √2)(3 - √2) =

=√(9/4) + 3² - (√2)² =

=3/2 +9 -2 =

= 1½ + 7 =

= 8½

68% = 8½

100% = x

x = 8½*100: 68

x = 17/2*100 :68

x = 17*50 : 68

x = 850 : 68

x = 12,5

5. OBLICZ 20 % liczby ¹/₉ ⁻¹ * √25 * √0.01 + 26 * (√5)² : √10²

Obliczam liczbę

x = (1/9)⁻¹*√25*√0,01 + 26*(√5)² : √10²

x = 9¹ *5*0,1+ 26*5 : 10

x = 4,5 + 13

x = 17,5

20% z x = 0,20*17.5 = 3,5

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heh

zad 1

$a)\ \sqrt{40}*\sqrt{10}=\sqrt{400}=20\\ b)\ \sqrt{12}:\sqrt{3}=\sqrt{12:3}=\sqrt{4}=2\\ c)\ \sqrt{800}:\sqrt{2}=\sqrt{800:2}=\sqrt{400}=20\\ d)\ \sqrt{800}*\sqrt{2}=\sqrt{800*2}=\sqrt{1600}=400$

zad 2

$a)\ \sqrt[3]{7}*\sqrt[3]{7}=\sqrt[3]{7*7}=\sqrt[3]{7^{2}}=\sqrt[3]{49}\\ b)\ \sqrt[3]{4}*\sqrt[3]{2}=\sqrt[3]{4*2}=\sqrt[3]{8}=\sqrt[3]{2^{3}}=2\\$

$c)\ \sqrt[3]{5}*\sqrt[3]{25}=\sqrt[3]{5*25}=\sqrt[3]{125}=\sqrt[3]{5^{3}}=5\\ d)\ \sqrt[3]{81}*\sqrt[3]{3}=\sqrt[3]{3^{4}}*\sqrt[3]{3}=\sqrt[3]{3^{5}}=\sqrt[3]{3^{3}*3^{2}}=3\sqrt[3]{9}$

$e)\ \sqrt[3]{4}*\sqrt[3]{6}:\sqrt[3]{3}=\sqrt[3]{4*6:3}=\sqrt[3]{8}=2\\ f)\ \frac{\sqrt[3]{2}}{\sqrt[3]{3}}*\sqrt[3]{81}=\frac{\sqrt[3]{2}}{\sqrt[3]{3}}*\sqrt[3]{3^{4}}=\sqrt[3]{2}*\sqrt[3]{3^{3}}=3\sqrt[3]{2}$

zad 3

$a)\ \sqrt{200}-\sqrt{32}+\sqrt{50}=\sqrt{2*10^{2}}-\sqrt{4^{2}*2}+\sqrt{5^{2}*2}=\\ 10\sqrt{2}-4\sqrt{2}+5\sqrt{2}=(10-4+5)\sqrt{2}=11\sqrt{2}$

$b)\ 2\sqrt{48}-3\sqrt{12}=2\sqrt{4^{2}*3}-3\sqrt{2^{2}*3}=2*4\sqrt{3}-3*2\sqrt{3}=\\ 8\sqrt{3}-6\sqrt{3}=2\sqrt{3}$

$c)\ \sqrt{50}+\sqrt{24}-\sqrt{18}+\sqrt{54}=\sqrt{5^{2}*2}+\sqrt{2^{2}*6}-\sqrt{3^{2}*2}+\sqrt{3^{2}*6}=\\ 5\sqrt{2}+2\sqrt{6}-3\sqrt{2}+3\sqrt{6}=2\sqrt{2}+6\sqrt{6}$