Square Roots: Using area

To determine the length of the sides of a square when the area is given, we proceed as follows:

• Step 1: Recall the formula for the area of a square: $\text{Area} = \text{side}^2$.
• Step 2: We need to find the side length, so we rearrange the formula to solve for the side: $\text{side} = \sqrt{\text{Area}}$.
• Step 3: Substitute the given area into the formula: $\text{side} = \sqrt{100}$.
• Step 4: Calculate the square root: $\sqrt{100} = 10$.

Therefore, the length of each side of the square is $10$.

We need to determine the side length of a square whose area is 16.

• Step 1: Set up the equation using the area formula for a square, $A = s^2$. Given the area $A = 16$, we have:
  $s^2 = 16$
• Step 2: Solve for $s$ by taking the square root of both sides:
  $s = \sqrt{16}$
• Step 3: Calculate the square root:
  $s = 4$

Since a side length cannot be negative, we take only the positive square root. Therefore, the side length of the square is $4$, which corresponds to choice 4.

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

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula to find the side length.
• Step 3: Perform the necessary calculations.

Now, let's work through each step:
Step 1: We are given the area of the square is 25 square units.
Step 2: We'll use the formula for the area of a square, $A = s^2$, where $s$ is the length of a side.
Step 3: Set up the equation $s^2 = 25$. To solve for $s$, take the square root of both sides: $s = \sqrt{25}$. This results in $s = 5$, considering the constraint that a side length must be non-negative.

Therefore, the solution to the problem is the side of the square is $s = 5$.

To calculate the length of the sides of a square given that its area is 144, we follow these steps:

• The problem gives us that the area of the square is 144. We are looking for the side length ($s$) of the square.
• We use the formula for the area of a square: $\text{Area} = \text{side}^2$. Substituting the given area, we have $144 = s^2$.
• We solve for $s$ by taking the square root of both sides: $s = \sqrt{144}$.
• Calculating $\sqrt{144}$, we find that $s = 12$.

Therefore, the length of the sides of the square is 12.

This corresponds to choice 4: $\sqrt{144}$, which emphasizes using the square root operation. However, the final calculation confirms that $s = 12$.

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

• Step 1: Apply the area formula $A = s^2$.
• Step 2: Set the given area equal to the formula: $256 = s^2$.
• Step 3: Solve for $s$ by taking the square root of both sides.

Now, let's work through each step:

Step 1: The formula for the area of a square is given by:

$A = s^2$

where $A$ is the area and $s$ is the side length. Given $A = 256$, we have:

$256 = s^2$

Step 2: To find $s$, take the square root of 256:

$s = \sqrt{256}$

Step 3: Calculate the square root:

$\sqrt{256} = 16$

Thus, the length of each side of the square is $16$.

Therefore, the solution to the problem is:

$16$

Checking against the given answer choices, our result corresponds to choice $\#2$: $16$.