Question

Вынесите множитель из-под знака корня:

Answer 1

$\sqrt[6]{64 {m}^{12} {n}^{7} } = \sqrt[6]{ {2}^{6} \times {m}^{2 \times 6} \times {n}^{6 + 1} } = \sqrt[6]{ {2}^{6} \times {( {m}^{2} )}^{6} \times {n}^{6} \times n} = \sqrt[6]{ {(2 \times {m}^{2} \times n)}^{6} \times n } = \sqrt[6]{ {(2 \times {m}^{2} \times n}^{6} } \times \sqrt[6]{n} = 2 {m}^{2} n \times \sqrt[6]{n}$

$\sqrt[7]{ {b}^{9} {c}^{8} } = \sqrt[7]{ {b}^{7 + 2} \times {c}^{7 + 1} } = \sqrt[7]{ {b}^{7} \times {b}^{2} \times {c}^{7} \times c } = \sqrt[7]{( {b}^{7} \times {c}^{7} ) \times {b}^{2} \times c} = \sqrt[7]{ {(b \times c)}^{7} \times {b}^{2} \times c } = \sqrt[7]{ {(bc)}^{7} } \times \sqrt[7]{ {b}^{2} c} = bc \times \sqrt[7]{ {b}^{2} c}$