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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.

5042 \frac{\sqrt{504}}{\sqrt{2}}

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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.

This problem has been solved

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