Найти значения выражений : (3√2) ² (5√3) ² (2√6) ²/36 6 / (2√3) ² (3√5) ²/15 √12•√270/√60 √180•√360/√80 √216•√80/√270 √8•√675/√60

Выполним математические преобразования:

1) (3√2) ² = 3² * (√2) ² = 9 * 2 = 18;

2) (5√3) ² = 5² * (√3) ² = 25 * 3 = 75;

3) (2√6) ²/36 = (2² * (√6) ²) / 36 = (4 * 6) / 36 = 24/36 = 12/18 = 6/9 = 2/3;

4) 6 / (2√3) 2 = 6 / (2² * (√3) ²) = 6 / (4 * 3) = 6/12 = 1/2;

5) (3√5) ²/15 = (3² * (√5) ²) / 15 = (9 * 5) / 15 = 45/15 = 3;

6) √12 * √270/√60 = √ (4 * 3) * √ (9 * 30) / √60 = (2 * √3 * 3 * √30) / √60 = (6 * √90) / √60 =

(6 * √3 * √30) / (√2 * √30) = (6 * √3) / √2 = (6 * √3 * √2) / 2 = 3 * √6;

7) √180 * √360/√80 = √18 * √10 * √36/√8 = 6 * √10 * √18/√8 = (6 * 3 * √10 * √2) / (2 * √2) = 9 * √10;

8) √216 * √80/√270 = (√216 * √8) / √27 = (√9 * √6 * √4 * √4 * √2) / (√9 * √3) = (3 * √6 * 2 * 2 * √2) / (3 * √3) = (12 * √12) / (3 * √3) = (12 * 2 * √3) / (3 * √3) = 8;

9) √8 * √675/√60 = (2 * √2 * √25 * √27) / (√4 * √15) = (10 * √2 * √27) / (2 * √15) = (5 * √2 * √3 * √9) / √15 = (15 * √6) / √15 = (15 * √6 * √15) / 15 = √6 * √15 = √90 = 3 * √10.