Square Root of Negative Numbers Practice Problems

The task is to find the square root of the number 100. The square root operation seeks a number which, when squared, equals the original number. For any positive integer, if $x^2 = 100$, then $x$ should be our answer.

Step 1: Recognize that 100 is a perfect square. This means there exists an integer $x$ such that $x \times x = 100$. Generally, we recall basic squares such as:

• $1^2 = 1$
• $2^2 = 4$
• $3^2 = 9$
• and so forth, up to $10^2$

Step 2: Checking integers, we find that:

$10^2 = 10 \times 10 = 100$

Step 3: Confirm the result: Since $10 \times 10 = 100$, then $\sqrt{100} = 10$.

Step 4: Compare with answer choices. Given that one of the choices is 10, and $\sqrt{100} = 10$, choice 1 is correct.

Therefore, the square root of 100 is 10.

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 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 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 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.