752 Вправа 752Алгебра 8 клас Бевз 2025 · § 15 · стор. 145

752. Обчисли, розклавши підкореневий вираз на множники.

а) ${\displaystyle \sqrt{625\cdot 10000}=}$${\displaystyle \sqrt{625}\cdot \sqrt{10000}}$=

=${\displaystyle 25\cdot 100=}$${\displaystyle 2500}$;

б) ${\displaystyle \sqrt{25\cdot 2025}=}$${\displaystyle \sqrt{25}\cdot \sqrt{2025}=}$${\displaystyle 5\cdot 45=}$${\displaystyle 225}$;

в) ${\displaystyle \sqrt{86436}=}$${\displaystyle \sqrt{4\cdot 9\cdot 2401}=}$${\displaystyle 2\cdot 3\cdot 49=}$${\displaystyle 294}$;

г) ${\displaystyle \sqrt{36\cdot 49\cdot 121}=}$${\displaystyle \sqrt{36}\cdot \sqrt{49}\cdot \sqrt{121}}$=

=${\displaystyle 6\cdot 7\cdot 11=}$${\displaystyle 462}$;

ґ) ${\displaystyle \sqrt{12\cdot 27}=}$${\displaystyle \sqrt{4\cdot 3\cdot 3\cdot 9}=}$${\displaystyle \sqrt{4\cdot 9\cdot 9}}$=

=${\displaystyle 2\cdot 3\cdot 3=}$${\displaystyle 18}$;

д) ${\displaystyle \sqrt{297\cdot 33}=}$${\displaystyle \sqrt{27\cdot 11\cdot 3\cdot 11}=}$${\displaystyle \sqrt{81\cdot 121}}$=

=${\displaystyle 9\cdot 11=}$${\displaystyle 99}$;

е) ${\displaystyle \sqrt{250\cdot 160}=}$${\displaystyle \sqrt{25\cdot 16\cdot 100}}$=

=${\displaystyle 5\cdot 4\cdot 10=}$${\displaystyle 200}$;

є) ${\displaystyle \sqrt{125\cdot 245}=}$${\displaystyle \sqrt{25\cdot 5\cdot 5\cdot 49}=}$${\displaystyle \sqrt{25\cdot 25\cdot 49}}$=

=${\displaystyle 5\cdot 5\cdot 7=}$${\displaystyle 175}$.