Square Root of a Negative Number

To solve this problem, we'll determine the square root of the number 4.

• Step 1: Recognize that the square root of a number is asking for a value that, when multiplied by itself, yields the original number. Here, we seek a number $y$ such that $y^2 = 4$.
• Step 2: Identify that $4$ is a perfect square. The numbers $2$ and $-2$ both satisfy the equation $2^2 = 4$ and $(-2)^2 = 4$.
• Step 3: We usually consider the principal square root, which is the non-negative version. Thus, $\sqrt{4} = 2$.

Therefore, the solution to the problem is 2, which corresponds to the correct choice from the given options.

To solve this problem, we want to find the square root of 9.

Step 1: Recognize that a square root is a number which, when multiplied by itself, equals the original number. Thus, we are seeking a number $x$ such that $x^2 = 9$.

Step 2: Note that 9 is a common perfect square: $9 = 3 \times 3$. Therefore, the square root of 9 is the number that, when multiplied by itself, gives 9. This number is 3.

Step 3: Since we are interested in the principal square root, we consider only the non-negative value. Hence, the principal square root of 9 is 3.

Therefore, the solution to the problem is $3$.

To determine the square root of 16, follow these steps:

• Identify that we are looking for the square root of 16, which is a number that, when multiplied by itself, equals 16.
• Recall the basic property of perfect squares: $4 \times 4 = 16$.
• Thus, the square root of 16 is 4.

Hence, the solution to the problem is the principal square root, which is $4$.

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

• Step 1: Understand the definition of a square root.
• Step 2: Identify which integer, when squared, gives 36.
• Step 3: Verify this integer meets the required condition.
• Step 4: Choose the correct answer from the given choices.

Now, let's work through each step:
Step 1: A square root of a number is a value that, when multiplied by itself, gives the original number. Here, we want $y$ such that $y^2 = 36$.
Step 2: We test integer values to find which one squared equals 36. Testing $y = 1, 2, 3, 4, 5,$ and $6$ gives:
- $1^2 = 1$
- $2^2 = 4$
- $3^2 = 9$
- $4^2 = 16$
- $5^2 = 25$
- $6^2 = 36$

Step 3: The integer $6$ satisfies $6^2 = 36$. Therefore, $\sqrt{36} = 6$.

Step 4: The correct choice from the given answer choices is 6 (Choice 4).

Hence, the square root of 36 is $\mathbf{6}$.

To solve this problem, we follow these steps:

• Step 1: Understand that finding the square root of a number means determining what number, when multiplied by itself, equals the original number.
• Step 2: Identify the numbers that could potentially be the square root of $49$. These are $\pm7$, but by convention, the square root function typically refers to the non-negative root.
• Step 3: Calculate $7 \times 7 = 49$. This confirms that $\sqrt{49} = 7$.
• Step 4: Verify using the problem's multiple-choice answers to ensure $7$ is among them, confirming choice number .

Therefore, the solution to the problem $\sqrt{49}$ is $7$.