Show how you get the simplest radical of 200
To find the simplest radical form of 200, we need to simplify it by factoring it into its prime factors.
First, we observe that 200 can be divided evenly by 2:
200 ÷ 2 = 100
Next, we continue factoring 100:
100 ÷ 2 = 50
Again, we factor 50:
50 ÷ 2 = 25
Finally, we reach a prime number, 25.
Therefore, the prime factors of 200 are 2 x 2 x 2 x 5 x 5.
To express this in simplest radical form, we group the prime factors in pairs:
2 x 2 x 5 x 5
Now, we can express 200 in simplest radical form as:
2 * 2 * 5 * 5 = sqrt(2 * 2 * 5 * 5) = 10 * sqrt(2)