Go step by step to reduce the radical. square root of 224

Answer 1

To reduce the square root of 224, we'll start by finding the prime factorization of 224.

224 can be written as 2 x 112.

Further breaking it down, 112 can be written as 2 x 56.

Breaking it down further, 56 can be written as 2 x 28.

Breaking it down even further, 28 can be written as 2 x 14.

Breaking it down one last time, 14 can be written as 2 x 7.

Putting it all together, we have: 224 = 2 x 2 x 2 x 2 x 2 x 7.

Now we can simplify the square root of 224:

√224 = √(2 x 2 x 2 x 2 x 2 x 7)

= 2 x 2 x √(2 x 7)

= 4√14

Therefore, the simplified form of the square root of 224 is 4√14.