747 Вправа 747Алгебра 8 клас Бевз 2025 · § 15 · стор. 144

747. Обчисли найраціональнішим способом.

а) ${\displaystyle \sqrt{100^2-96^2}=}$${\displaystyle \sqrt{(100-96)(100+96)}}$=

=${\displaystyle \sqrt{4\cdot 196}=}$${\displaystyle 2\cdot 14=}$${\displaystyle 28}$;

б) ${\displaystyle \sqrt{61^2-60^2}=}$${\displaystyle \sqrt{(61-60)(61+60)}}$=

=${\displaystyle \sqrt{1\cdot 121}=}$${\displaystyle 1\cdot 11=}$${\displaystyle 11}$;

в) ${\displaystyle \sqrt{37^2-12^2}=}$${\displaystyle \sqrt{(37-12)(37+12)}}$=

=${\displaystyle \sqrt{25\cdot 49}=}$${\displaystyle 5\cdot 7=}$${\displaystyle 35}$;

г) ${\displaystyle \sqrt{6,8^2-3,2^2}=}$${\displaystyle \sqrt{(6,8-3,2)(6,8+3,2)}}$=

=${\displaystyle \sqrt{3,6\cdot 10}=}$${\displaystyle \sqrt{36}=}$${\displaystyle 6}$;

ґ) ${\displaystyle \sqrt{1,3^2-0,66^2}=}$${\displaystyle \sqrt{(1,3-0,66)(1,3+0,66)}}$=

=${\displaystyle \sqrt{0,64\cdot 1,96}=}$${\displaystyle 0,8\cdot 1,4=}$${\displaystyle 1,12}$;

д) ${\displaystyle \sqrt{3,73^2-2,52^2}}$=

=${\displaystyle \sqrt{(3,73-2,52)(3,73+2,52)}=}$${\displaystyle \sqrt{1,21\cdot 6,25}}$=

=${\displaystyle 1,1\cdot 2,5=}$${\displaystyle 2,75}$.