Simplify the radical expression. Show all your steps.

Question

363−−−√−327−−√

Answer 1

First, simplify the given expression:

√363 - √327

Now, find the prime factorization of each number:

363 = 3 * 121
327 = 3 * 109

Now, rewrite the expression with the prime factorization:

√(3 * 121) - √(3 * 109)

Now, simplify the expression by taking the square root of the perfect squares:

11√3 - (√3)(√109)

Finally, combine like terms:

11√3 - √327