Корень 12 умножить корень 270/корень 60

To simplify this expression, let's break it down step by step:

√12 * √270 / √60

First, let's simplify the square roots individually:

√12 = √(4 * 3) = √4 * √3 = 2√3

√270 = √(9 * 30) = √9 * √30 = 3√30

√60 = √(4 * 15) = √4 * √15 = 2√15

Now substitute these simplified square roots back into the original expression:

2√3 * 3√30 / 2√15

Next, cancel out common factors:

2/2 = 1

Now the expression becomes:

√3 * 3√30 / √15

To multiply square roots, you can multiply the numbers outside the square root sign and multiply the numbers inside the square root sign:

√3 * 3√30 / √15 = 3√(3 * 30) / √15 = 3√90 / √15

Now let's simplify the square roots again:

√90 = √(9 * 10) = √9 * √10 = 3√10

√15 remains as it is.

Finally, substitute these simplified expressions back into the original expression:

3√10 / √15