Nxdkylie
Rozwiązane

POTRZEBUJĘ NA TERAZ
oblicz
A) ✓20*✓125
B)✓3*3*3 * ✓7*3*3
C) ✓363/√3
D)³√3*³√9
E)³√11*11*5 * ³√5*5*11
F)³√54/³√250​



Odpowiedź :

Anita13122007

a)

[tex] \sqrt{20} \times \sqrt{125} = \sqrt{2500} = 50[/tex]

b)

[tex] \sqrt{3 \times 3 \times 3} \times \sqrt{7 \times 3 \times 3} = \sqrt{1701} = 9 \sqrt{21} [/tex]

c)

[tex] \frac{ \sqrt{363} }{ \sqrt{3} } = \sqrt{121} = 11[/tex]

d)

[tex] \sqrt[3]{3} \times \sqrt[3]{9} = \sqrt[3]{27} = 3[/tex]

e)

[tex] \sqrt[3]{11 \times 11 \times 5} \times \sqrt[3]{5 \times 5 \times 11} = \sqrt[3]{166375} = 55[/tex]

f)

[tex] \frac{ \sqrt[3]{54} }{ \sqrt[3]{250} } = \frac{ \sqrt[3]{27} }{ \sqrt[3]{125} } = \frac{3}{ \sqrt[3]{125} } = \frac{3}{5} [/tex]

Basetla

[tex]A) \ \sqrt{20}\cdot\sqrt{125} = \sqrt{20\cdot125} = \sqrt{2500} = \sqrt{50^{2}} = 50\\\\\\B) \ \sqrt{3\cdot3\cdot3}\cdot\sqrt{7\cdot3\cdot3}} = \sqrt{3^{2}\cdot3}\cdot\sqrt{3^{2}\cdot7} = 3\sqrt{3}\cdot3\sqrt{7} = 9\sqrt{3\cdot7} = 9\sqrt{21}\\\\\\C) \ \frac{\sqrt{363}}{\sqrt{3}} =\sqrt{\frac{363}{3}} = \sqrt{121} = \sqrt{11^{2}} = 11\\\\\\D) \ \sqrt[3]{3}\cdot\sqrt[3]{9} = \sqrt[3]{3\cdot9} = \sqrt[3]{27} = \sqrt[3]{3^{3}} = 3[/tex]

[tex]E) \ \sqrt[3]{11\cdot11\cdot5}\cdot\sqrt[3]{5\cdot5\cdot11}=\sqrt[3]{11\cdot11\cdot5\cdot5\cdot5\cdot11} = \sqrt[3]{11^{3}\cdot5^{3}} = 11\cdot5 = 55\\\\\\F) \ \frac{\sqrt[3]{54}}{\sqrt[3]{250}} = \sqrt[3]{\frac{54}{250}} = \sqrt[3]{\frac{27}{125}} = \sqrt[3]{\frac{3^{3}}{5^{3}}} = \frac{3}{5}[/tex]