Questions: Rationalize the denominator and simplify. sqrt(6/30)

Solution Steps

To rationalize the denominator and simplify the given expression, we need to follow these steps:

1. Simplify the fraction inside the square root.
2. Take the square root of the simplified fraction.
3. If necessary, rationalize the denominator by multiplying the numerator and the denominator by the square root of the denominator.

First, we simplify the fraction \(\frac{6}{30}\) by finding the greatest common divisor (GCD) of 6 and 30, which is 6. Dividing both the numerator and the denominator by 6, we get: \[ \frac{6}{30} = \frac{1}{5} \]

Next, we take the square root of the simplified fraction: \[ \sqrt{\frac{1}{5}} = \frac{\sqrt{1}}{\sqrt{5}} = \frac{1}{\sqrt{5}} \]

To rationalize the denominator, we multiply both the numerator and the denominator by \(\sqrt{5}\): \[ \frac{1}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{5}}{5} \]

Final Answer