Simplify the Square Root: Solving √(9/36) Step by Step

To solve this problem, we'll follow these steps:

• Step 1: Simplify the fraction within the square root, if possible.
• Step 2: Apply the square root quotient property $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$.
• Step 3: Calculate the square roots of the resulting numbers.
• Step 4: Simplify the fraction, if necessary.

Now, let's work through each step:

Step 1: Simplify the fraction $\frac{9}{36}$.
We notice that both 9 and 36 have a common factor of 9. So, we simplify:

$\frac{9}{36} = \frac{1}{4}$

Step 2: Apply the square root quotient property:

$\sqrt{\frac{9}{36}} = \sqrt{\frac{1}{4}}$

Now address the square root of the simplified fraction:

$\sqrt{\frac{1}{4}} = \frac{\sqrt{1}}{\sqrt{4}}$

Step 3: Calculate the square roots:

$\sqrt{1} = 1$
$\sqrt{4} = 2$

Step 4: Simplify the fraction:

$\frac{1}{2}$

Therefore, the solution to the problem is $\frac{1}{2}$.