Question

1.Włącz czynnik przed znak pierwiastka i zapisz krócej: np. √32=√16*2=4√2

5√3=

1/2√12=

7√2=

0,1√2000=

6√5/6=

4³√2=

2.Uporządkuj rosnąco liczby.

a)3√3, 2√6, √29, 4√2

b)3√4, 4√3, 8, ³√216

3.Oblicz.

2*³√125-√64=

3√36+5³√-64=

(2/3√6)²

4.Rozłóż na czynniki pierwsze i oblicz wartoci pierwiastków.

√324=

√576=

√484=

³√-729=

5.Oblicz.

√2*2*3*2*3*2

√2 * √18=

³√5*2*5*5*2*2=

√300 * √3=

√200*√2=

³√27*8=

√3^4 * 4^2=

√5*√20=

7√2*6√8=

Answer 1

zad.1

5√3= √25*√3=√75

1/2√12=√0,25 * √12 =√3

7√2=√49 * √2 = √98

0,1√2000= √0,01 * √2000 = √20

6√5/6=√36 * √5/6 = √30

4³√2= ∛64 *∛2 = ∛128

 

zad.2

a)3√3, 2√6, √29, 4√2

(3√3)² = 27

(2√6)² = 24

(√29)² = 29

(4√2)² = 32

24<27<29<32 => 2√6<3√3<√29<4√2

 

b)3√4, 4√3, 8, ³√216

3√4 = 3 * 2 = 6   6²=36

(4√3)² = 48

8² = 64

∛216 = 2∛27 = 2 * 3 = 6    6²=36

36=36<48<64 => 3√4=∛216 < 4√3 <8

 

zad.3

2 * ³√125 - √64 = 2 * 5 - 8 = 10 - 8 = 2

3√36 + 5³√-64 = 3 * 6 + 5 * (-4) = 18 + (-20) = 18 - 20 = -2

(2/3√6)² = 4/9 * 6 = 8/3 = 2 i 2/3

zad.4

√324= √9 * √36 = 3 * 6 = 18

√576= √9 * √64 = 3 * 8 = 24

√484= √4 * √121 = 2 * 11 = 22

³√-729= ∛27 * ∛-27 = 3 * (-3) = -27

 

zad.5

√2*2*3*2*3*2 = √4 * √4 * √9 = 2*2*3=12

√2 * √18= √2 * 3√2 = 3*2=6

³√5*2*5*5*2*2= 5 * 2 = 10

√300 * √3= √100 * √3 * √3 = 10 *3 =30

√200*√2= √2 * √ 100 * √ 2= 2*10 =20

³√27*8= 3*2=6

√3^4 * 4^2= 3*3*4=36

√5*√20= 5*√4=5*2=10

7√2*6√8= 7√2 * 12√2 = 84 * 2 = 168