Question
What is the quotient of the following expression state to answering simplest radical form ritalization the denominator if necessary radical of 36/400
Answers
GPT-4o mini
To simplify the expression \(\frac{\sqrt{36}}{\sqrt{400}}\), we can follow these steps:
1. **Find the square roots:**
- \(\sqrt{36} = 6\)
- \(\sqrt{400} = 20\)
2. **Express the quotient:**
\[
\frac{\sqrt{36}}{\sqrt{400}} = \frac{6}{20}
\]
3. **Simplify the fraction:**
\[
\frac{6}{20} = \frac{3}{10} \quad \text{(dividing numerator and denominator by 2)}
\]
Since the denominator \(10\) is not a radical, no further rationalization is necessary.
Thus, the final answer in simplest form is:
\[
\frac{3}{10}
\]
1. **Find the square roots:**
- \(\sqrt{36} = 6\)
- \(\sqrt{400} = 20\)
2. **Express the quotient:**
\[
\frac{\sqrt{36}}{\sqrt{400}} = \frac{6}{20}
\]
3. **Simplify the fraction:**
\[
\frac{6}{20} = \frac{3}{10} \quad \text{(dividing numerator and denominator by 2)}
\]
Since the denominator \(10\) is not a radical, no further rationalization is necessary.
Thus, the final answer in simplest form is:
\[
\frac{3}{10}
\]