Fraction:
5√30
-------
30
Step 1: Simplify the expression under the radical sign.
5√30 = √(30*5) = √150
Step 2: Rewrite the fraction with the simplified radical in the numerator.
√150
------
30
Step 3: Rationalize the denominator by multiplying both the numerator and denominator by √30.
√150 * √30 = √4500 = 30√5
30 * √30 = 30√30 = 30 * 5 = 150
So, the simplified radical expression by rationalizing the denominator is:
30√5
-----
150
Which simplifies to:
√5
---
5