567 Вправа 567Алгебра 8 клас Тарасенкова 2025 · § 13 · стор. 163

567. Розкладіть на множники:

1) ${\displaystyle \sqrt{12}+\sqrt{72}=}$${\displaystyle 2\sqrt{3}+6\sqrt{2}=}$${\displaystyle 2\left(\sqrt{3}+3\sqrt{2}\right)}$;

2) ${\displaystyle \sqrt{45}-2\sqrt{27}=}$${\displaystyle 3\sqrt{5}-6\sqrt{3}=}$${\displaystyle 3\left(\sqrt{5}-2\sqrt{3}\right)}$;

3) ${\displaystyle \sqrt{2}+2=}$${\displaystyle \sqrt{2}+\sqrt{2}\cdot \sqrt{2}=}$${\displaystyle \sqrt{2}\left(1+\sqrt{2}\right)}$;

4) ${\displaystyle 3\sqrt{11}-11=}$${\displaystyle 3\sqrt{11}-\sqrt{11}\cdot \sqrt{11}=}$${\displaystyle \sqrt{11}\left(3-\sqrt{11}\right)}$;

5) ${\displaystyle 2\sqrt{7}-14=}$${\displaystyle 2\sqrt{7}-2\sqrt{7}\cdot \sqrt{7}=}$${\displaystyle 2\sqrt{7}\left(1-\sqrt{7}\right)}$;

6) ${\displaystyle -36+\sqrt{6}=}$${\displaystyle -6\sqrt{6}\cdot \sqrt{6}+\sqrt{6}=}$${\displaystyle \sqrt{6}\left(1-6\sqrt{6}\right)}$;

7) ${\displaystyle \sqrt{15}+3\sqrt{30}+\sqrt{45}=}$${\displaystyle \sqrt{15}+3\sqrt{15}\cdot \sqrt{2}+\sqrt{15}\cdot \sqrt{3}=}$${\displaystyle \sqrt{15}\left(1+3\sqrt{2}+\sqrt{3}\right)}$;

8) ${\displaystyle 5\sqrt{10}-\sqrt{50}+\sqrt{200}=}$${\displaystyle 5\sqrt{10}-5\sqrt{2}+10\sqrt{2}=}$${\displaystyle 5\sqrt{10}+5\sqrt{2}=}$${\displaystyle 5\sqrt{2}\left(\sqrt{5}+1\right)}$;

9) ${\displaystyle 12-\sqrt{18}-\sqrt{27}=}$${\displaystyle 12-3\sqrt{2}-3\sqrt{3}=}$${\displaystyle 3\left(4-\sqrt{2}-\sqrt{3}\right)}$.