$\sqrt{-m^9} = \sqrt{(-m)^8 * (-m)} = |-m|^4 * \sqrt{-m} = m^4\sqrt{-m}$

$\sqrt{a^4b^{13}} = \sqrt{a^4 * b^{12} * b} = \sqrt{(a^2)^2} * \sqrt{(b^6)^2} * \sqrt{b} = a^2b^6\sqrt{b}$, если a ≠ 0

$\sqrt{4x^6y} = \sqrt{4 * (x^3)^2 * y} = \sqrt{2^2} * \sqrt{(x^3)^2} * \sqrt{y} = 2 * |x^3| * \sqrt{y} = -2x^3\sqrt{y}$, если x < 0

$\sqrt{m^7n^7} = \sqrt{m^6 * m * n^6 * n} = \sqrt{(m^3)^2} * \sqrt{m} * \sqrt{(n^3)^2} * \sqrt{n} = |m^3| * |n^3| * \sqrt{mn} = m^3n^3\sqrt{mn}$, если m ≤ 0, n ≤ 0

$\sqrt{45x^3y^{14}} = \sqrt{9 * 5 * x^2 * x * (y^{7})^2} = \sqrt{3^2} * \sqrt{5} * \sqrt{x^2} * \sqrt{x} * \sqrt{(y^{7})^2} = 3 * |y^7| * \sqrt{5x} = -3y^7\sqrt{5x}$, если y < 0

$\sqrt{64a^2b^{9}} = \sqrt{8^2 * a^2 * b^{8} * b} = \sqrt{8^2} * \sqrt{a^2} * \sqrt{(b^4)^2} * \sqrt{b} = 8 * |a| * |b^4| * \sqrt{b} = 8ab^4\sqrt{b}$, если a > 0

$\sqrt{242m^{11}b^{18}} = \sqrt{2 * 121 * m^{10} * m * (b^{9})^2} = \sqrt{2} * \sqrt{11^2} * \sqrt{(m^5)^2} * \sqrt{m} * \sqrt{(b^9)^2} = 11 * |m^5| * |b^9| * \sqrt{2m} = -11m^5b^9\sqrt{2m}$, если b < 0

$\sqrt{-m^2n^{2}p^{15}} = \sqrt{-1 * m^2 * n^{2} * p^{14} * p} = \sqrt{m^2} * \sqrt{n^2} * \sqrt{(p^7)^2} * \sqrt{-p} = |m^2| * |n^2| * |p^7| * \sqrt{-p} = m^2n^2p^7\sqrt{-p}$, если m > 0, n < 0