I need help simplifying the radical
(IN RADICAL FORM ONLY)
What's the square root of 224?
Can you please show how you got the answer so I can learn how to do it myself next time please.
since √x^2 = x, you want to factor out all the perfect squares.
224 = 16*14
so,
√224 = √(4^2 * 14) = 4√14
To simplify the square root of 224, we can look for perfect square factors of 224.
Step 1: Prime factorize 224.
The prime factorization of 224 is 2^5 * 7.
Step 2: Group the prime factors in pairs.
Since we are taking the square root, we will group the prime factors in pairs of two.
224 = (2^2) * (2^1) * 7
Step 3: Simplify each pair.
Since 2^2 = 4 and 7 cannot be simplified further, we have:
√224 = √(2^2 * (2^1) * 7)
= (2√(2^1 * 7))
= 2√(14)
So, the square root of 224, in radical form only, is 2√14.
Now you know the method to simplify a square root in radical form.