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Go step by step to reduce the radical.
Square Root 200

Go step by step to reduce the radical. Square Root 200-example-1

2 Answers

5 votes

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).

User Christian Borck
by
8.3k points
3 votes

Answer:

10 root 2

Explanation:

root 200 = root 2 × root 100 = 10 root 2

User Nikola Mitic
by
8.1k points

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