4. Найдите значение выражения: 4.1. $\frac{\sqrt{36a^9b^5}}{\sqrt{ab}}$, при a = 9, b = 4 4.2. $\frac{\sqrt{36a^34b}}{\sqrt{ab}}$, при a = 7, b = 5 4.3. $\frac{\sqrt{16a^5}\cdot \sqrt{36b}}{\sqrt{ab}}$, при a = 4, b = 5 4.4. $\frac{\sqrt{25a^3}\cdot \sqrt{9b}}{\sqrt{ab}}$, при a = 2, b = 9 4.5. $\frac{\sqrt{9a}\cdot \sqrt{16b^5}}{\sqrt{ab}}$, при a = 5, b = 2

Question

Вопрос: $Фото задания: 4. Найдите значение выражения: 4.1. $\frac{\sqrt{36a^9b^5}}{\sqrt{ab}}$, при a = 9, b = 4 4.2.…$ Фото задания

Accepted Answer

$\frac{\sqrt{36a^9b^5}}{\sqrt{ab}} = \sqrt{\frac{36a^9b^5}{ab}} = \sqrt{36a^8b^4} = 6a^4b^2 = 6 \cdot 9^4 \cdot 4^2 = 6 \cdot 6561 \cdot 16 = 629856$
$\frac{\sqrt{36a^34b}}{\sqrt{ab}} = \sqrt{\frac{36a^34b}{ab}} = \sqrt{36a^2b^3} = 6ab\sqrt{b} = 6 \cdot 7 \cdot 5 \sqrt{5} = 210\sqrt{5}$
$\frac{\sqrt{16a^5}\cdot \sqrt{36b}}{\sqrt{ab}} = \sqrt{\frac{16a^5 \cdot 36b}{ab}} = \sqrt{16a^4 \cdot 36b^0} = \sqrt{16a^4 \cdot 36} = 4a^2 \cdot 6 = 24a^2 = 24 \cdot 4^2 = 24 \cdot 16 = 384$
$\frac{\sqrt{25a^3}\cdot \sqrt{9b}}{\sqrt{ab}} = \sqrt{\frac{25a^3 \cdot 9b}{ab}} = \sqrt{25a^2 \cdot 9b^0} = \sqrt{25a^2 \cdot 9} = 5a \cdot 3 = 15a = 15 \cdot 2 = 30$
$\frac{\sqrt{9a}\cdot \sqrt{16b^5}}{\sqrt{ab}} = \sqrt{\frac{9a \cdot 16b^5}{ab}} = \sqrt{9a^0 \cdot 16b^4} = \sqrt{9 \cdot 16b^4} = 3 \cdot 4b^2 = 12b^2 = 12 \cdot 2^2 = 12 \cdot 4 = 48$

Ответ: 4.1. 629856, 4.2. 210√5, 4.3. 384, 4.4. 30, 4.5. 48.