Square Roots: Simple exercise

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 $7$.

To solve this problem, we'll determine the square root of 64, following these steps:

• Step 1: Identify the number whose square root we need to find. The number given is 64.
• Step 2: Determine which number, when multiplied by itself, equals 64.
• Step 3: Recall that $8 \times 8 = 64$.

Now, let's work through each step:

Step 1: We are tasked with finding $\sqrt{64}$. The problem involves identifying the number which, when squared, results in 64.
Step 2: To find this number, we'll check our knowledge of squares. We know that 8 is a significant integer whose square results in 64.
Step 3: Compute: $8 \times 8 = 64$. Hence, $8$ meets the requirement.

We find that the solution to the problem is $\sqrt{64} = 8$.

To solve this problem, follow these steps:

• Step 1: Understand that the square root of a number $n$ is a value that, when multiplied by itself, equals $n$.
• Step 2: Identify the number whose square is 81. Since $9 \times 9 = 81$, the square root of 81 is 9.

Therefore, the square root of 81 is $9$.

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 need to determine the square root of 25.

• Step 1: The square root operation asks us to find a number that, when multiplied by itself, equals the given number, 25.
• Step 2: Consider what number times itself equals 25. We note that $5 \times 5 = 25$.
• Step 3: Thus, the square root of 25 is 5.

Therefore, the solution to the problem is $\sqrt{25} = 5$.

The correct answer is choice 2: 5.

To solve the problem of finding the square root of 121, let's follow these steps:

• Step 1: Understand that we need to find a number $x$ such that $x^2 = 121$.
• Step 2: Recognize that 121 is a perfect square. Specifically, $11 \times 11 = 121$.
• Step 3: Therefore, the square root of 121 is clearly $11$.

Thus, the solution to the problem is $11$.

To solve this problem, we proceed with the following steps:

• Step 1: Identify that the problem asks for the square root of 144.
• Step 2: Use the concept of square roots, where $\sqrt{n} = x$ implies $x^2 = n$.
• Step 3: Check for a perfect square whose square equals 144.

Now, let's solve the problem:

Step 1: We need the square root $\sqrt{144}$.

Step 2: Recall that $x^2 = 144$. We need to find $x$.

Step 3: Recognize that 144 is a perfect square and find $x$ such that $x^2 = 144$. Through either calculation or prior knowledge, we know:
$12^2 = 144$.

Therefore, the square root of 144 is $\sqrt{144} = 12$.

Thus, the solution to the problem is $\mathbf{12}$.

To solve for the square root of 169, we need to determine which whole number, when multiplied by itself, equals 169.

• Step 1: Recall that squaring a number means multiplying the number by itself. Therefore, we need to find a number $n$ such that $n \times n = 169$.
• Step 2: Check known square values or perform some calculations: $13 \times 13 = 169$.
• Step 3: Verify that $13^2 = 169$, confirming that 13 is the square root.

Therefore, the solution to the problem is $\sqrt{169} = 13$.

The given problem requires us to determine the square root of 196. To solve this, we need to find a number that, when multiplied by itself, equals 196.

Let's evaluate whether 196 is a perfect square. We know that:

• $14 \times 14 = 196$

Therefore, the square root of 196 is $14$, since 14 multiplied by itself gives 196.

Thus, the correct answer is $14$, which corresponds to choice 1.

To solve the problem, we will follow these steps:

• Step 1: Identify the perfect squares near 225.
• Step 2: Calculate to find which integer when squared equals 225.

Now, let's work through the steps:

Step 1: The perfect squares around 225 are $196 = 14^2$, $225 = 15^2$, and $256 = 16^2$.
Step 2: We calculate $15^2 = 15 \times 15 = 225$, therefore, $\sqrt{225} = 15$.

Therefore, the solution to the problem is $\sqrt{225} = 15$.

Accordingly, the correct answer choice is option 2: 15.

To solve the problem of finding $\sqrt{256}$, we will determine a number that, when squared, results in 256.

The operation we are performing is finding the square root, which is defined as follows: if $x^2 = n$, then $x$ is the square root of $n$.

First, consider the list of perfect squares: 1 (because $1^2 = 1$), 4 (because $2^2 = 4$), 9 (because $3^2 = 9$), 16 (because $4^2 = 16$), all the way up to 256 which needs to be checked.

Let's test the number 16:
$16^2 = 16 \times 16 = 256$

This confirms that 16 is the square root of 256.

Therefore, the solution to the problem is $\sqrt{256} = 16$.