Question

Oblicz
Zadanie w załączniku

Answer 1

Odpowiedź:

[tex]\huge \boxed {a)~~\sqrt[3]{-6,4} \cdot \sqrt[3]{10} =-4}[/tex]

[tex]\huge \boxed {b)~~\sqrt[3]{25} \cdot \sqrt[3]{5} =5}[/tex]

[tex]\huge \boxed {c)~~\sqrt[3]{16} \cdot \sqrt[3]{32} =8}[/tex]

[tex]\huge \boxed {d)~~\dfrac{\sqrt[3]{-32} }{\sqrt[3]{4} } =-2}[/tex]

[tex]\huge \boxed {e)~~\dfrac{\sqrt[3]{54} }{\sqrt[3]{-2} } =-3}[/tex]

[tex]\huge \boxed {f)~~\dfrac{\sqrt[3]{750} }{\sqrt[3]{48} } =1\dfrac{2}{3}}[/tex]

Szczegółowe wyjaśnienie:

Korzystamy ze wzorów:

• [tex]\sqrt[n]{x^{n}} =x,~~zal.~~x\geq 0[/tex]
• [tex]\sqrt[n]{x} \cdot \sqrt[n]{y} =\sqrt[n]{x\cdot y} ,~~zal.~~x\geq 0,y\geq 0[/tex]
• [tex]\dfrac{\sqrt[n]{x} }{\sqrt[n]{y} } =\sqrt[n]{\dfrac{x}{y} } ,~~zal.~~x\geq 0, y > 0[/tex]
• [tex]\dfrac{x^{n}}{y^{n}} =\left (\dfrac{x}{y} \right)^{n},~~zal.~~y\neq 0[/tex]

Obliczamy :

[tex]a)~~\sqrt[3]{-6,4} \cdot \sqrt[3]{10} =\sqrt[3]{(-6,4)\cdot 10} =\sqrt[3]{-64} =\sqrt[3]{(-4)^{3}}=-4[/tex]

[tex]b)~~\sqrt[3]{25} \cdot \sqrt[3]{5} =\sqrt[3]{25\cdot 5} =\sqrt[3]{125} =\sqrt[3]{5^{3}}=5[/tex]

[tex]c)~~\sqrt[3]{16} \cdot \sqrt[3]{32} =\sqrt[3]{16\cdot 32} =\sqrt[3]{512} =\sqrt[3]{8^{3}}=8[/tex]

[tex]d)~~\dfrac{\sqrt[3]{-32} }{\sqrt[3]{4} } =\sqrt[3]{\dfrac{-32\!\!\!\!\!\diagup^8}{4\!\!\!\!\diagup_1} } =\sqrt[3]{-8} =\sqrt[3]{(-2)^{3}} =-2[/tex]

[tex]e)~~\dfrac{\sqrt[3]{54} }{\sqrt[3]{-2} } =\sqrt[3]{\dfrac{54\!\!\!\!\!\diagup^2^7}{-2\!\!\!\!\diagup_1} } =\sqrt[3]{-27} =\sqrt[3]{(-3)^{3}} =-3[/tex]

[tex]f)~~\dfrac{\sqrt[3]{750} }{\sqrt[3]{48} } =\sqrt[3]{\dfrac{750}{48} } =\sqrt[3]{\dfrac{125\cdot 6\!\!\!\!\diagup^1}{8\cdot 6\!\!\!\!\diagup_1} } =\sqrt[3]{\dfrac{5^{3}}{2^{3}} } =\sqrt[3]{\left(\dfrac{5}{3} \right)^{3}} =\dfrac{5}{3} =1\dfrac{2}{3}[/tex]