92. Найдите значение выражения: 1) √75⋅27; 2) √72⋅200; 3) √1,6⋅14,4; 4) √1690⋅6,4.

1) $$ \sqrt{75 \cdot 27} = \sqrt{25 \cdot 3 \cdot 9 \cdot 3} = \sqrt{25 \cdot 9 \cdot 9} = 5 \cdot 3 \cdot 3 = 45 $$

2) $$ \sqrt{72 \cdot 200} = \sqrt{36 \cdot 2 \cdot 100 \cdot 2} = \sqrt{36 \cdot 100 \cdot 4} = 6 \cdot 10 \cdot 2 = 120 $$

3) $$ \sqrt{1.6 \cdot 14.4} = \sqrt{\frac{16}{10} \cdot \frac{144}{10}} = \frac{4}{ \sqrt{10} } \cdot \frac{12}{ \sqrt{10} } = \frac{48}{10} = 4.8 $$

4) $$ \sqrt{1690 \cdot 6.4} = \sqrt{169 \cdot 10 \cdot \frac{64}{10}} = \sqrt{169 \cdot 64} = 13 \cdot 8 = 104 $$