Корень 12 умножить корень 270/корень 60

To solve this expression, we can simplify each part separately and then multiply the results:

First, let's simplify each square root: √12 = √(4 * 3) = √4 * √3 = 2√3

√270 = √(9 * 30) = √9 * √30 = 3√30

√60 = √(4 * 15) = √4 * √15 = 2√15

Now, we multiply the simplified square roots: 2√3 * 3√30 / 2√15

Multiplying the coefficients: 2 * 3 = 6

Multiplying the terms with the same radicand: √3 * √30 = √(3 * 30) = √90 = √(9 * 10) = 3√10

√15 remains the same.

Putting it all together:

6 * (3√10 / 2√15) = 6/2 * (3√10 / √15) = 3 * (3√10 / √15) = 9√10 / √15 = (9√10 * √15) / √15 * √15 = (9√(10 * 15)) / 15 = 9√150 / 15

Therefore, the simplified result is 9√150 / 15.