Odpowiedź:
a)
6(√10)² = 6 * 10 = 60
b)
2√7 * 5√7 = 2 * 5 * (√7)² = 10 * 7 = 70
c)
(2/3√15)² = (2/3)² * (√15)² = 4/9 * 15 = 4/3 * 5 = 20/3 = 6 2/3
d)
∛(25 * √25) = ∛(25 * 5) = ∛(5² * 5) = ∛5²⁺¹ = ∛5³ = 5
3.
[tex]a) \ \ 6(\sqrt{10})^{2} =6\cdot(10^{\frac{1}{2}})^{2} = 6\cdot10^{\frac{1}{2}\cdot2} = 6\cdot10 = \boxed{60}\\\\b) \ \ 2\sqrt{7}\cdot5\sqrt{7} = 2\cdot5\cdot\sqrt{7}\cdot\sqrt{7} = 10\cdot(\sqrt{7})^{2} = 10\cdot7 = \boxed{70}[/tex]
[tex]c) \ \ (\frac{2}{3}\sqrt{15})^{2} =(\frac{2}{3})^{2}\cdot(\sqrt{15})^{2} = \frac{4}{9}\cdot15 = \frac{4\cdot5}{3} = \frac{20}{3} = \boxed{6\frac{2}{3}}\\\\d) \ \ \sqrt[3]{25+\sqrt{25}} = \sqrt[3]{25+5} = \boxed{\sqrt[3]{30}}[/tex]
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Odpowiedź:
a)
6(√10)² = 6 * 10 = 60
b)
2√7 * 5√7 = 2 * 5 * (√7)² = 10 * 7 = 70
c)
(2/3√15)² = (2/3)² * (√15)² = 4/9 * 15 = 4/3 * 5 = 20/3 = 6 2/3
d)
∛(25 * √25) = ∛(25 * 5) = ∛(5² * 5) = ∛5²⁺¹ = ∛5³ = 5
Verified answer
3.
[tex]a) \ \ 6(\sqrt{10})^{2} =6\cdot(10^{\frac{1}{2}})^{2} = 6\cdot10^{\frac{1}{2}\cdot2} = 6\cdot10 = \boxed{60}\\\\b) \ \ 2\sqrt{7}\cdot5\sqrt{7} = 2\cdot5\cdot\sqrt{7}\cdot\sqrt{7} = 10\cdot(\sqrt{7})^{2} = 10\cdot7 = \boxed{70}[/tex]
[tex]c) \ \ (\frac{2}{3}\sqrt{15})^{2} =(\frac{2}{3})^{2}\cdot(\sqrt{15})^{2} = \frac{4}{9}\cdot15 = \frac{4\cdot5}{3} = \frac{20}{3} = \boxed{6\frac{2}{3}}\\\\d) \ \ \sqrt[3]{25+\sqrt{25}} = \sqrt[3]{25+5} = \boxed{\sqrt[3]{30}}[/tex]