Упр.17.30 ГДЗ Мерзляк Поляков 8 класс (Алгебра)

1. $$\sqrt{-m^9}=\sqrt{m^8\cdot(-m)}=m^4\sqrt{-m}.$$
2. $$\sqrt{96(a-3)^5}=\sqrt{16\cdot 6\cdot (a-3)^4\cdot (a-3)}=4(a-3)^2\sqrt{6(a-3)}.$$
3. $$\sqrt{a^4b^{13}}=a^2b^6\sqrt{b}.$$
4. $$\sqrt{4x^6y}=-2x^3\sqrt{y}.$$
5. $$\sqrt{(a+1)^6(a^2+1)^5}=-(a+1)^3(a^2+1)^2\sqrt{a^2+1}.$$
6. $$\sqrt{m^7n^7}=\sqrt{(-m^3)(-n^3)\cdot mn}=m^3n^3\sqrt{mn}.$$
7. $$\sqrt{45x^3y^{14}}=\sqrt{9\cdot 5\cdot x^2\cdot x\cdot y^{14}}=-3xy^7\sqrt{5x}.$$
8. $$\sqrt{64a^2b^9}=8ab^4\sqrt{b}.$$
9. $$\sqrt{242m^{11}b^{18}}=\sqrt{121\cdot 2\cdot m^{10}\cdot m\cdot b^{18}}=-11m^5b^9\sqrt{2m}.$$
10. $$\sqrt{-m^2p^{15}}=mp^7\sqrt{-p}.$$
11. $$\sqrt{x^5(y-1)^4}=x^2(y-1)^2\sqrt{x}.$$
12. $$\sqrt{-y^7(x+2)^8}=-y^3(x+2)^4\sqrt{-y}.$$

Ответ

1. $$m^4\sqrt{-m}$$
2. $$4(a-3)^2\sqrt{6(a-3)}$$
3. $$a^2b^6\sqrt{b}$$
4. $$-2x^3\sqrt{y}$$
5. $$-(a+1)^3(a^2+1)^2\sqrt{a^2+1}$$
6. $$m^3n^3\sqrt{mn}$$
7. $$-3xy^7\sqrt{5x}$$
8. $$8ab^4\sqrt{b}$$
9. $$-11m^5b^9\sqrt{2m}$$
10. $$mp^7\sqrt{-p}$$
11. $$x^2(y-1)^2\sqrt{x}$$
12. $$-y^3(x+2)^4\sqrt{-y}$$