Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify the radical expression. Show all your steps.
363−−−√−327−−√
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To simplify the radical expression √363 - √327, we need to find the prime factors of 363 and 327.
Prime factors of 363:
363 = 3 * 121
= 3 * 11 * 11
= 3 * 11^2
Prime factors of 327:
327 = 3 * 109
Now we can simplify the expression:
√363 - √327
= √(3 * 11^2) - √(3 * 109)
= 11√3 - 3√109
So, the simplified radical expression is 11√3 - 3√109.