657 Вправа 657Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 194

657. Спростіть вираз:

1) ${\displaystyle \sqrt{\frac{45a^3}{b}}\cdot \sqrt{\frac{5a}{b^{-1}}}=}$${\displaystyle \sqrt{\frac{45a^3\cdot 5a}{b\cdot b^{-1}}}=}$${\displaystyle \sqrt{225a^4}=}$${\displaystyle 15a^2}$;

2) ${\displaystyle \sqrt{\frac{45a^3}{b}}:\sqrt{\frac{5a}{b^{-1}}}=}$${\displaystyle \sqrt{\frac{45a^3\cdot b^{-1}}{b\cdot 5a}}=}$${\displaystyle \sqrt{\frac{9a^2}{b^2}}=}$${\displaystyle \frac{3\left|a\right|}{\left|b\right|}}$;

3) ${\displaystyle \sqrt{\frac{12x^5}{y^{-2}}}:\sqrt{\frac{y^6}{3x^{-7}}}=}$${\displaystyle \sqrt{\frac{12x^5\cdot 3x^{-7}}{y^{-2}\cdot y^6}}=}$${\displaystyle \sqrt{\frac{36x^{-2}}{y^4}}=}$${\displaystyle \sqrt{\frac{36}{x^2{y}^4}}=}$${\displaystyle \frac{6}{\left|x\right|y^2}}$;

4) ${\displaystyle \sqrt{\frac{12x^5}{y^{-2}}}\cdot \sqrt{\frac{y^6}{3x^{-7}}}=}$${\displaystyle \sqrt{\frac{12x^5{y}^6}{3y^{-2}{x}^{-7}}}=}$${\displaystyle \sqrt{4x^{12}{y}^8}=}$${\displaystyle 2x^6{y}^4}$;

5) ${\displaystyle \sqrt{1\frac{8}{9}\cdot \frac{xy}{z^{-2}}}\cdot \sqrt{\frac{x{y}^{-5}}{17z^4}}=}$${\displaystyle \sqrt{\frac{17}{9}\cdot \frac{xy\cdot x{y}^{-5}}{z^{-2}\cdot 17z^4}}=}$${\displaystyle \sqrt{\frac{x^2{y}^{-4}}{9z^2}}=}$${\displaystyle \frac{\left|x\right|}{3\left|z\right|y^2}}$;

6) ${\displaystyle \sqrt{\frac{a{b}^3}{c{d}^{-4}}}\cdot \sqrt{\frac{c^{-3}}{a^{-5}}}\cdot \sqrt{\frac{d^{-4}}{c^{-4}{a}^6}}=}$${\displaystyle \sqrt{a^{1+5-6}{b}^3{c}^{-1-3+4}{d}^{4-4}}=}$${\displaystyle \sqrt{b^3}=}$${\displaystyle b\sqrt{b}}$.