The simplified radical of 240 is 6sqrt(6).
The image you sent shows how to reduce the radical of 240.
To reduce the radical of a number, you need to find the largest perfect square that is a factor of the number. In the case of 240, the largest perfect square that is a factor of 240 is 120.
Once you have found the largest perfect square that is a factor of the number, you can rewrite the number as a product of the perfect square and another number. In the case of 240, we can rewrite it as 120 * 2.
Now, we can use the product rule for radicals to simplify the radical. The product rule for radicals states that the radical of a product is equal to the product of the radicals of the individual numbers.
So, the radical of 240 can be simplified as follows:
sqrt(240) = sqrt(120 * 2) = sqrt(120) * sqrt(2)
To simplify the radical of 120, we can repeat the process above. The largest perfect square that is a factor of 120 is 36. So, we can rewrite 120 as 36 * 3.
sqrt(120) = sqrt(36 * 3) = sqrt(36) * sqrt(3) = 6 * sqrt(3)
Now, we can put everything together to get the simplified radical of 240:
sqrt(240) = sqrt(120 * 2) = sqrt(120) * sqrt(2) = 6 * sqrt(3) * sqrt(2) = 6sqrt(6)
Therefore, the reduced radical of 240 is 6sqrt(6).