Questions: Use the quotient rule to simplify the expression. √(16/9)

Transcript text: Use the quotient rule to simplify the expression. \[ \sqrt{\frac{16}{9}} \]

Solution

Step 1: Apply the Quotient Rule

To simplify the expression \( \sqrt{\frac{16}{9}} \), we apply the quotient rule for square roots, which states that:

\[ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \]

In this case, we have:

\[ \sqrt{\frac{16}{9}} = \frac{\sqrt{16}}{\sqrt{9}} \]

Step 2: Calculate the Square Roots

Next, we calculate the square roots of the numerator and the denominator:

\[ \sqrt{16} = 4 \quad \text{and} \quad \sqrt{9} = 3 \]

Step 3: Divide the Square Roots

Now, we divide the results from Step 2:

\[ \frac{\sqrt{16}}{\sqrt{9}} = \frac{4}{3} \approx 1.3333 \]

Thus, the simplified result of the expression \( \sqrt{\frac{16}{9}} \) is

\[ \boxed{\frac{4}{3}} \]

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