Express in simplest radical form.start fraction, square root of, 504, end square root, divided by, square root of, 2, end square root, end fraction2 504
Question
Express in simplest radical form.start fraction, square root of, 504, end square root, divided by, square root of, 2, end square root, end fraction2 504
Solution
First, let's simplify the square root of 504.
The prime factorization of 504 is 2^3 * 3^2 * 7.
We can pair the factors to take out of the square root: (2^2, 3^2) and leave the rest (2, 7) inside the square root.
So, √504 simplifies to 23√(2*7) = 6√14.
Next, we divide this by √2.
So, we have 6√14 / √2.
To simplify this, we multiply the numerator and the denominator by √2 to get rid of the square root in the denominator.
This gives us 6√28 / 2.
Finally, we simplify this to get 3√28.
So, √504 / √2 in simplest radical form is 3√28.
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