What are those mysterious square roots that often confuse students and complicate their lives? The truth is that to understand them, we need to grasp the concept of the inverse operation.
What are those mysterious square roots that often confuse students and complicate their lives? The truth is that to understand them, we need to grasp the concept of the inverse operation.
When we solve an exercise like , it's clear that times (that is, multiplying the number by itself) results in . This is the concept of a power, or to be more precise, a square power, which to apply, we must multiply the figure or the number by itself.
The concept of "square root" refers to the inverse operation of squaring numbers.
That is, if we have and we want to find the value of , what we need to do is perform an identical operation on both sides of the equation.
So, we have: and the result is .
\( \sqrt{4}= \)
\( \sqrt{9}= \)
\( \sqrt{16}= \)
\( \sqrt{36}= \)
\( \sqrt{49}= \)
To solve this problem, we'll determine the square root of the number 4.
Therefore, the solution to the problem is 2, which corresponds to the correct choice from the given options.
2
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 such that .
Step 2: Note that 9 is a common perfect square: . 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:
Hence, the solution to the problem is the principal square root, which is .
4
To solve this problem, we'll follow these steps:
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 such that .
Step 2: We test integer values to find which one squared equals 36. Testing and gives:
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Step 3: The integer satisfies . Therefore, .
Step 4: The correct choice from the given answer choices is 6 (Choice 4).
Hence, the square root of 36 is .
6
To solve this problem, we follow these steps:
Therefore, the solution to the problem is .
7
\( \sqrt{64}= \)
\( \sqrt{81}= \)
\( \sqrt{100}= \)
\( \sqrt{25}= \)
\( \sqrt{36}= \)
To solve this problem, we'll determine the square root of 64, following these steps:
Now, let's work through each step:
Step 1: We are tasked with finding . 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: . Hence, meets the requirement.
We find that the solution to the problem is .
8
To solve this problem, follow these steps:
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 , then should be our answer.
Step 1: Recognize that 100 is a perfect square. This means there exists an integer such that . Generally, we recall basic squares such as:
Step 2: Checking integers, we find that:
Step 3: Confirm the result: Since , then .
Step 4: Compare with answer choices. Given that one of the choices is 10, and , choice 1 is correct.
Therefore, the square root of 100 is 10.
10
To solve this problem, we need to determine the square root of 25.
Therefore, the solution to the problem is .
The correct answer is choice 2: 5.
5
Let's solve the problem step by step:
The square root of a number is a value that, when multiplied by itself, equals . This is written as .
We are looking for a number such that . This translates to finding .
We know that . Therefore, the principal square root of is .
Thus, the solution to the problem is .
Among the given choices, the correct one is: Choice 1: .
6
\( \sqrt{64}= \)
Solve the following exercise:
\( \sqrt{x^2}= \)
\( \sqrt{441}= \)
\( \sqrt{x}=14 \)
\( \sqrt{x}=15 \)
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: To find the square root of 64, we seek a number that, when multiplied by itself, equals 64.
Step 2: Consider the sequence of perfect squares: , , , , , , , .
Step 3: We see that . Therefore, the square root of 64 is 8.
Therefore, the solution to this problem is .
8
Solve the following exercise:
In order to simplify the given expression, we will use two laws of exponents:
a. The definition of root as an exponent:
b. The law of exponents for power of a power:
Let's start with converting the square root to an exponent using the law mentioned in a':
We'll continue using the law of exponents mentioned in b' and perform the exponent operation on the term in parentheses:
Therefore, the correct answer is answer a'.
The root of 441 is 21.
To solve this problem, we'll follow the steps below:
Step 3: Calculate the square of 14:
Therefore, the value of is 196.
Comparing our solution with the provided choices, choice 3 () is the correct match.
Thus, the solution to the problem is .
196
To solve the given problem, we will follow these steps:
Now, let's work through each step:
Step 1: We are given .
To eliminate the square root, square both sides of the equation:
Step 2: Simplify both sides:
On the left, .
On the right, .
This gives us the equation:
Thus, the solution to the problem is .
225