A.
[tex] \sqrt[3]{125} \times \sqrt{ \frac{1}{25} } = 5 \times \frac{1}{5} = 1[/tex]
[tex] \sqrt{1 \frac{24}{25} } \div \sqrt{ \frac{49}{625} } = \sqrt{ \frac{49}{25} } \div \sqrt{ \frac{49}{625} } = \frac{7}{5} \div \frac{7}{25} = \frac{7}{5} \times \frac{25}{7} = 5[/tex]
Odp. A jest błędna
B.
[tex] \sqrt{ {2}^{2} \times {5}^{2} } = \sqrt{4 \times 25} = \sqrt{100} = 10 [/tex]
[tex] \sqrt[3]{ {10}^{3} \div {5}^{3} } = \sqrt[3]{1000 \div 125} = \sqrt[3]{8} = 2[/tex]
Odp. B jest błędna
C.
[tex] {2}^{3} \times \sqrt[3]{ - \frac{1}{8} } = 8 \times - \frac{1}{2} = - 4[/tex]
[tex] {2}^{2} \times \sqrt{ \frac{1}{4} } = 4 \times \frac{1}{2} = 2[/tex]
Odp. C jest błędna
D.
[tex] \sqrt{32} \div \sqrt{2} \times \sqrt[3]{8} = \sqrt{32 \div 2} \times 2 = \sqrt{16} \times 2 = 4 \times 2 = 8[/tex]
[tex] \sqrt[3]{2} \times \sqrt[3]{4} \times \sqrt{25 - 9} = \sqrt[3]{2 \times 4} \times \sqrt{16} = \sqrt[3]{8} \times 4 = 2 \times 4 = 8[/tex]
Odp. D jest prawidłowa
