simplify the radical expression by rationalizing the denominator

Question

5/sqrt30

Answer 1

To simplify the radical expression 5/sqrt(30), we need to rationalize the denominator.

First, factor 30 into its prime factors:
30 = 2 * 3 * 5

Now we can rewrite the expression as:
5/sqrt(2 * 3 * 5)

Since the square root of (2 * 3 * 5) is equal to sqrt(2) * sqrt(3) * sqrt(5), we can rewrite the expression as:
5/(sqrt(2) * sqrt(3) * sqrt(5))

Now, we can rationalize the denominator by multiplying the numerator and denominator by sqrt(30), which is the square root of 30:
(5 * sqrt(30))/(sqrt(2) * sqrt(3) * sqrt(5) * sqrt(30))

This simplifies to:
5 * sqrt(30) / (sqrt(2 * 3 * 5 * 30))
5 * sqrt(30) / sqrt(30)
5