Question

Simplify the radical expression by rationalizing the denominator.

Start Fraction 5 over Start Root 30 End Root End Fraction
(1 point)
Responses

30Start Root 5 End Root
30 Image with alt text: Start Root 5 End Root

square root of 30
Image with alt text: square root of 30

start fraction start root 180 end root over 30 end fraction
Image with alt text: start fraction start root 180 end root over 30 end fraction

start fraction start root 30 end root over 6 end fraction

Answer 1

[AI-generated answer — Bot GPT 3.5]

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