Корень 12 умножить корень 270/корень 60

To simplify the expression "square root of 12 multiplied by square root of 270 divided by square root of 60," we can first simplify each individual square root.

√12 is equal to √(4 × 3), which can be further simplified to 2√3.

√270 is equal to √(9 × 30), which simplifies to 3√30.

√60 is equal to √(4 × 15), which simplifies to 2√15.

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

2√3 × 3√30 / 2√15

Next, we can combine the numerical coefficients:

(2 × 3)√3√30 / 2√15

Simplifying further:

6√(3 × 30) / 2√15

6√90 / 2√15

Since 6 and 2 have a common divisor of 2, we can cancel it out:

(6/2)√90 / √15

3√90 / √15

Now, looking for common factors within the square roots:

√3 × √(3 × 10) / √15

Simplifying further:

√3 × √30 / √15

Now, multiplying and dividing the terms under the square roots:

√(3 × 30) / √15

√90 / √15

Finally, combining the square roots:

√(90/15)

Simplifying the fraction:

√6

So, the simplified expression is √6.