Упростите выражение:
1) $\sqrt{9a^{16}}$;
2) $\sqrt{0,81d^6}$, если d ≥ 0;
3) $-5\sqrt{4x^2}$, если x ≤ 0;
4) $-0,1\sqrt{100z^{10}}$, если z ≥ 0;
5) $\sqrt{p^6q^8}$, если p ≥ 0;
6) $\sqrt{25m^{34}n^{38}}$, если m ≤ 0, n ≤ 0;
7) $ab^2\sqrt{a^4b^{18}c^{22}}$, если b ≥ 0, c ≤ 0;
8) $-\frac{8m^3p^4}{k^2}\sqrt{\frac{625k^{30}p^{40}}{144m^6}}$, если m <0, k > 0.
$\sqrt{9a^{16}} = \sqrt{(3a^{8})^2} = |3a^8| = 3a^8$
$\sqrt{0,81d^6} = \sqrt{(0,9d^3)^2}= |0,9d^3| = 0,9d^3$, если d ≥ 0
$-5\sqrt{4x^2} = -5\sqrt{(2x)^2} = -5 * |2x| = -5 * (-2x) = 10x$, если x ≤ 0
$-0,1\sqrt{100z^{10}} = -0,1\sqrt{(10z^{5})^2} = -0,1 * |10z^5| = -0,1 * 10z^5 = -z^5$, если z ≥ 0
$\sqrt{p^6q^8} = \sqrt{(p^3q^4)^2} = |p^3q^4| = p^3q^4$, если p ≥ 0
$\sqrt{25m^{34}n^{38}} = \sqrt{(5m^{17}n^{19})^2} = |5m^{17}n^{19}| = 5 * (-m^17) * (-n^19) = 5m^{17}n^{19}$, если m ≤ 0, n ≤ 0
$ab^2\sqrt{a^4b^{18}c^{22}} = ab^2\sqrt{(a^2b^{9}c^{11})^2} = ab^2 * |a^2b^{9}c^{11}| = ab^2 * a^2b^9 * (-c^{11}) = -a^3b^{11}c^{11}$, если b ≥ 0, c ≤ 0
$-\frac{8m^3p^4}{k^2}\sqrt{\frac{625k^{30}p^{40}}{144m^6}} = -\frac{8m^3p^4}{k^2} * \frac{\sqrt{625k^{30}p^{40}}}{\sqrt{144m^6}} = -\frac{8m^3p^4}{k^2} * \frac{\sqrt{(25k^{15}p^{20})^2}}{\sqrt{(12m^3)^2}} = -\frac{8m^3p^4}{k^2} * \frac{|25k^{15}p^{20}|}{|12m^3|} = -\frac{8m^3p^4}{k^2} * \frac{25k^{15}p^{20}}{-12m^3} = \frac{2p^4}{1} * \frac{25k^{13}p^{20}}{3} = \frac{50k^{13}p^{24}}{3}$, если m <0, k > 0
Пожауйста, оцените решение
