Question

ОЧЕНЬ СРОЧНО!!!!!!!!!!!!!!!!!!!

Answer 1

$\frac{2}{3} \sqrt{45} = \frac{2}{3} \sqrt{9 \times 5} = \frac{2}{3} \times 3 \sqrt{5} = 2 \sqrt{5}$

$\frac{1}{2} \sqrt{120} = \frac{1}{2} \sqrt{4 \times 30} = \frac{1}{2} \times 2 \sqrt{30} = \sqrt{30}$

$\sqrt{ \frac{8}{27} } = \frac{ \sqrt{4 \times 2} }{ \sqrt{9 \times 3} } = \frac{2 \sqrt{2} }{3 \sqrt{3} } = \frac{2 \sqrt{2} \times \sqrt{3} }{3 \sqrt{3} \times \sqrt{3} } = \frac{2 \sqrt{6} }{9}$

$\sqrt{ \frac{40}{63} } = \frac{ \sqrt{4 \times 10} }{ \sqrt{9 \times 7} } = \frac{2 \sqrt{10} }{3 \sqrt{7} } = \frac{2 \sqrt{10 } \times \sqrt{7} }{3 \sqrt{7} \times \sqrt{7} } = \frac{2 \sqrt{70} }{3 \times 7} = \frac{2 \sqrt{70} }{21}$

$\sqrt{1 \frac{1}{12} } = \frac{ \sqrt{13} }{ \sqrt{12} } = \frac{ \sqrt{13} }{2 \sqrt{3} } = \frac{ \sqrt{13} \times \sqrt{3} }{2 \sqrt{3} \times \sqrt{3} } = \frac{ \sqrt{39} }{2 \times 3} = \frac{ \sqrt{39} }{6}$

$\sqrt{10 \frac{1}{8} } = \frac{ \sqrt{81} }{ \sqrt{8} } = \frac{9}{2 \sqrt{2} } = \frac{9 \times \sqrt{2} }{2 \sqrt{2} \times \sqrt{2} } = \frac{9 \sqrt{2} }{2 \times 2} = \frac{9 \sqrt{2} }{4}$

$\sqrt{ {x}^{15} y {}^{2} } = y \sqrt{x {}^{14} \times x } = x {}^{7} y \sqrt{x}$

$\sqrt{ \frac{50m {}^{4} n {}^{3} }{9r {}^{4} } } = \frac{ \sqrt{25 \times 2m {}^{4}n {}^{2} \times n} }{ \sqrt{3 \times 3r {}^{4} } } = \frac{5m {}^{2}n \sqrt{2n} }{3r {}^{2} }$