Square Roots: Simple exercise

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 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 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 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 $11$.

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 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, 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.

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 $\sqrt{256}$, 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 $\sqrt{256} = 16$.

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 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 $\sqrt{169} = 13$.

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 $9$.